On modules whose coclosed submodules are isomorphic to direct summands

Abstract Inspired by the notion of virtually extending module, in this work we have proposed and investigated the behaviours of virtually lifting module as the dual of virtually extending module. Several properties of this structure have been discussed and got that virtually lifting module is a %$D_...
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Gespeichert in:

Autor*in:	Das, L. K. [verfasserIn] Patel, M. K.

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2022

Schlagwörter:	Virtually semi-simple module module Principally -lifting module

Anmerkung:	© Indian National Science Academy 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Übergeordnetes Werk:	Enthalten in: Proceedings of the Indian National Science Academy - Indian National Science Academy, 2022, 88(2022), 4 vom: 31. Okt., Seite 790-795
Übergeordnetes Werk:	volume:88 ; year:2022 ; number:4 ; day:31 ; month:10 ; pages:790-795

Links:	Volltext

DOI / URN:	10.1007/s43538-022-00131-z

Katalog-ID:	SPR051151995

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520			\|a Abstract Inspired by the notion of virtually extending module, in this work we have proposed and investigated the behaviours of virtually lifting module as the dual of virtually extending module. Several properties of this structure have been discussed and got that virtually lifting module is a %$D_{12}%$ module. It is observed that for a V ring R, a module M is virtually lifting iff it is lifting. Moreover, we have defined virtually %$D_{2}%$ module as a proper extension of %$D_{2}%$ module, and seen that virtually %$D_{2}%$ modules is inherited by direct summands. Finally, we have investigated principally h-lifting module and proved that finite direct sum of principally h-lifting modules are principally h-lifting if each components are principally relatively projective.
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912			\|a GBV_ILN_152
912			\|a GBV_ILN_161
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912			\|a GBV_ILN_171
912			\|a GBV_ILN_187
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_250
912			\|a GBV_ILN_281
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912			\|a GBV_ILN_2007
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912			\|a GBV_ILN_2011
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912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
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912			\|a GBV_ILN_2031
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912			\|a GBV_ILN_2110
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allfields	10.1007/s43538-022-00131-z doi (DE-627)SPR051151995 (SPR)s43538-022-00131-z-e DE-627 ger DE-627 rakwb eng Das, L. K. verfasserin aut On modules whose coclosed submodules are isomorphic to direct summands 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Indian National Science Academy 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Inspired by the notion of virtually extending module, in this work we have proposed and investigated the behaviours of virtually lifting module as the dual of virtually extending module. Several properties of this structure have been discussed and got that virtually lifting module is a %$D_{12}%$ module. It is observed that for a V ring R, a module M is virtually lifting iff it is lifting. Moreover, we have defined virtually %$D_{2}%$ module as a proper extension of %$D_{2}%$ module, and seen that virtually %$D_{2}%$ modules is inherited by direct summands. Finally, we have investigated principally h-lifting module and proved that finite direct sum of principally h-lifting modules are principally h-lifting if each components are principally relatively projective. Virtually semi-simple module (dpeaa)DE-He213 module (dpeaa)DE-He213 module (dpeaa)DE-He213 module (dpeaa)DE-He213 Principally (dpeaa)DE-He213 -lifting module (dpeaa)DE-He213 Patel, M. K. (orcid)0000-0003-1010-261X aut Enthalten in Proceedings of the Indian National Science Academy Indian National Science Academy, 2022 88(2022), 4 vom: 31. Okt., Seite 790-795 (DE-627)78783341X (DE-600)2773381-6 2454-9983 nnns volume:88 year:2022 number:4 day:31 month:10 pages:790-795 https://dx.doi.org/10.1007/s43538-022-00131-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 AR 88 2022 4 31 10 790-795
spelling	10.1007/s43538-022-00131-z doi (DE-627)SPR051151995 (SPR)s43538-022-00131-z-e DE-627 ger DE-627 rakwb eng Das, L. K. verfasserin aut On modules whose coclosed submodules are isomorphic to direct summands 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Indian National Science Academy 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Inspired by the notion of virtually extending module, in this work we have proposed and investigated the behaviours of virtually lifting module as the dual of virtually extending module. Several properties of this structure have been discussed and got that virtually lifting module is a %$D_{12}%$ module. It is observed that for a V ring R, a module M is virtually lifting iff it is lifting. Moreover, we have defined virtually %$D_{2}%$ module as a proper extension of %$D_{2}%$ module, and seen that virtually %$D_{2}%$ modules is inherited by direct summands. Finally, we have investigated principally h-lifting module and proved that finite direct sum of principally h-lifting modules are principally h-lifting if each components are principally relatively projective. Virtually semi-simple module (dpeaa)DE-He213 module (dpeaa)DE-He213 module (dpeaa)DE-He213 module (dpeaa)DE-He213 Principally (dpeaa)DE-He213 -lifting module (dpeaa)DE-He213 Patel, M. K. (orcid)0000-0003-1010-261X aut Enthalten in Proceedings of the Indian National Science Academy Indian National Science Academy, 2022 88(2022), 4 vom: 31. Okt., Seite 790-795 (DE-627)78783341X (DE-600)2773381-6 2454-9983 nnns volume:88 year:2022 number:4 day:31 month:10 pages:790-795 https://dx.doi.org/10.1007/s43538-022-00131-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 AR 88 2022 4 31 10 790-795
allfields_unstemmed	10.1007/s43538-022-00131-z doi (DE-627)SPR051151995 (SPR)s43538-022-00131-z-e DE-627 ger DE-627 rakwb eng Das, L. K. verfasserin aut On modules whose coclosed submodules are isomorphic to direct summands 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Indian National Science Academy 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Inspired by the notion of virtually extending module, in this work we have proposed and investigated the behaviours of virtually lifting module as the dual of virtually extending module. Several properties of this structure have been discussed and got that virtually lifting module is a %$D_{12}%$ module. It is observed that for a V ring R, a module M is virtually lifting iff it is lifting. Moreover, we have defined virtually %$D_{2}%$ module as a proper extension of %$D_{2}%$ module, and seen that virtually %$D_{2}%$ modules is inherited by direct summands. Finally, we have investigated principally h-lifting module and proved that finite direct sum of principally h-lifting modules are principally h-lifting if each components are principally relatively projective. Virtually semi-simple module (dpeaa)DE-He213 module (dpeaa)DE-He213 module (dpeaa)DE-He213 module (dpeaa)DE-He213 Principally (dpeaa)DE-He213 -lifting module (dpeaa)DE-He213 Patel, M. K. (orcid)0000-0003-1010-261X aut Enthalten in Proceedings of the Indian National Science Academy Indian National Science Academy, 2022 88(2022), 4 vom: 31. Okt., Seite 790-795 (DE-627)78783341X (DE-600)2773381-6 2454-9983 nnns volume:88 year:2022 number:4 day:31 month:10 pages:790-795 https://dx.doi.org/10.1007/s43538-022-00131-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 AR 88 2022 4 31 10 790-795
allfieldsGer	10.1007/s43538-022-00131-z doi (DE-627)SPR051151995 (SPR)s43538-022-00131-z-e DE-627 ger DE-627 rakwb eng Das, L. K. verfasserin aut On modules whose coclosed submodules are isomorphic to direct summands 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Indian National Science Academy 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Inspired by the notion of virtually extending module, in this work we have proposed and investigated the behaviours of virtually lifting module as the dual of virtually extending module. Several properties of this structure have been discussed and got that virtually lifting module is a %$D_{12}%$ module. It is observed that for a V ring R, a module M is virtually lifting iff it is lifting. Moreover, we have defined virtually %$D_{2}%$ module as a proper extension of %$D_{2}%$ module, and seen that virtually %$D_{2}%$ modules is inherited by direct summands. Finally, we have investigated principally h-lifting module and proved that finite direct sum of principally h-lifting modules are principally h-lifting if each components are principally relatively projective. Virtually semi-simple module (dpeaa)DE-He213 module (dpeaa)DE-He213 module (dpeaa)DE-He213 module (dpeaa)DE-He213 Principally (dpeaa)DE-He213 -lifting module (dpeaa)DE-He213 Patel, M. K. (orcid)0000-0003-1010-261X aut Enthalten in Proceedings of the Indian National Science Academy Indian National Science Academy, 2022 88(2022), 4 vom: 31. Okt., Seite 790-795 (DE-627)78783341X (DE-600)2773381-6 2454-9983 nnns volume:88 year:2022 number:4 day:31 month:10 pages:790-795 https://dx.doi.org/10.1007/s43538-022-00131-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 AR 88 2022 4 31 10 790-795
allfieldsSound	10.1007/s43538-022-00131-z doi (DE-627)SPR051151995 (SPR)s43538-022-00131-z-e DE-627 ger DE-627 rakwb eng Das, L. K. verfasserin aut On modules whose coclosed submodules are isomorphic to direct summands 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Indian National Science Academy 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Inspired by the notion of virtually extending module, in this work we have proposed and investigated the behaviours of virtually lifting module as the dual of virtually extending module. Several properties of this structure have been discussed and got that virtually lifting module is a %$D_{12}%$ module. It is observed that for a V ring R, a module M is virtually lifting iff it is lifting. Moreover, we have defined virtually %$D_{2}%$ module as a proper extension of %$D_{2}%$ module, and seen that virtually %$D_{2}%$ modules is inherited by direct summands. Finally, we have investigated principally h-lifting module and proved that finite direct sum of principally h-lifting modules are principally h-lifting if each components are principally relatively projective. Virtually semi-simple module (dpeaa)DE-He213 module (dpeaa)DE-He213 module (dpeaa)DE-He213 module (dpeaa)DE-He213 Principally (dpeaa)DE-He213 -lifting module (dpeaa)DE-He213 Patel, M. K. (orcid)0000-0003-1010-261X aut Enthalten in Proceedings of the Indian National Science Academy Indian National Science Academy, 2022 88(2022), 4 vom: 31. Okt., Seite 790-795 (DE-627)78783341X (DE-600)2773381-6 2454-9983 nnns volume:88 year:2022 number:4 day:31 month:10 pages:790-795 https://dx.doi.org/10.1007/s43538-022-00131-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 AR 88 2022 4 31 10 790-795
language	English
source	Enthalten in Proceedings of the Indian National Science Academy 88(2022), 4 vom: 31. Okt., Seite 790-795 volume:88 year:2022 number:4 day:31 month:10 pages:790-795
sourceStr	Enthalten in Proceedings of the Indian National Science Academy 88(2022), 4 vom: 31. Okt., Seite 790-795 volume:88 year:2022 number:4 day:31 month:10 pages:790-795
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Virtually semi-simple module module Principally -lifting module
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container_title	Proceedings of the Indian National Science Academy
authorswithroles_txt_mv	Das, L. K. @@aut@@ Patel, M. K. @@aut@@
publishDateDaySort_date	2022-10-31T00:00:00Z
hierarchy_top_id	78783341X
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author	Das, L. K.
spellingShingle	Das, L. K. misc Virtually semi-simple module misc module misc Principally misc -lifting module On modules whose coclosed submodules are isomorphic to direct summands
authorStr	Das, L. K.
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topic_title	On modules whose coclosed submodules are isomorphic to direct summands Virtually semi-simple module (dpeaa)DE-He213 module (dpeaa)DE-He213 Principally (dpeaa)DE-He213 -lifting module (dpeaa)DE-He213
topic	misc Virtually semi-simple module misc module misc Principally misc -lifting module
topic_unstemmed	misc Virtually semi-simple module misc module misc Principally misc -lifting module
topic_browse	misc Virtually semi-simple module misc module misc Principally misc -lifting module
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title	On modules whose coclosed submodules are isomorphic to direct summands
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title_full	On modules whose coclosed submodules are isomorphic to direct summands
author_sort	Das, L. K.
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author_browse	Das, L. K. Patel, M. K.
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author-letter	Das, L. K.
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title_sort	on modules whose coclosed submodules are isomorphic to direct summands
title_auth	On modules whose coclosed submodules are isomorphic to direct summands
abstract	Abstract Inspired by the notion of virtually extending module, in this work we have proposed and investigated the behaviours of virtually lifting module as the dual of virtually extending module. Several properties of this structure have been discussed and got that virtually lifting module is a %$D_{12}%$ module. It is observed that for a V ring R, a module M is virtually lifting iff it is lifting. Moreover, we have defined virtually %$D_{2}%$ module as a proper extension of %$D_{2}%$ module, and seen that virtually %$D_{2}%$ modules is inherited by direct summands. Finally, we have investigated principally h-lifting module and proved that finite direct sum of principally h-lifting modules are principally h-lifting if each components are principally relatively projective. © Indian National Science Academy 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
abstractGer	Abstract Inspired by the notion of virtually extending module, in this work we have proposed and investigated the behaviours of virtually lifting module as the dual of virtually extending module. Several properties of this structure have been discussed and got that virtually lifting module is a %$D_{12}%$ module. It is observed that for a V ring R, a module M is virtually lifting iff it is lifting. Moreover, we have defined virtually %$D_{2}%$ module as a proper extension of %$D_{2}%$ module, and seen that virtually %$D_{2}%$ modules is inherited by direct summands. Finally, we have investigated principally h-lifting module and proved that finite direct sum of principally h-lifting modules are principally h-lifting if each components are principally relatively projective. © Indian National Science Academy 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
abstract_unstemmed	Abstract Inspired by the notion of virtually extending module, in this work we have proposed and investigated the behaviours of virtually lifting module as the dual of virtually extending module. Several properties of this structure have been discussed and got that virtually lifting module is a %$D_{12}%$ module. It is observed that for a V ring R, a module M is virtually lifting iff it is lifting. Moreover, we have defined virtually %$D_{2}%$ module as a proper extension of %$D_{2}%$ module, and seen that virtually %$D_{2}%$ modules is inherited by direct summands. Finally, we have investigated principally h-lifting module and proved that finite direct sum of principally h-lifting modules are principally h-lifting if each components are principally relatively projective. © Indian National Science Academy 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
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title_short	On modules whose coclosed submodules are isomorphic to direct summands
url	https://dx.doi.org/10.1007/s43538-022-00131-z
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author2	Patel, M. K.
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doi_str	10.1007/s43538-022-00131-z
up_date	2024-07-03T20:06:35.181Z
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fullrecord_marcxml	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR051151995</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230509120713.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">230508s2022 xx \|\|\|\|\|o 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s43538-022-00131-z</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR051151995</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s43538-022-00131-z-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Das, L. K.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">On modules whose coclosed submodules are isomorphic to direct summands</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2022</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Indian National Science Academy 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Inspired by the notion of virtually extending module, in this work we have proposed and investigated the behaviours of virtually lifting module as the dual of virtually extending module. Several properties of this structure have been discussed and got that virtually lifting module is a %$D_{12}%$ module. It is observed that for a V ring R, a module M is virtually lifting iff it is lifting. Moreover, we have defined virtually %$D_{2}%$ module as a proper extension of %$D_{2}%$ module, and seen that virtually %$D_{2}%$ modules is inherited by direct summands. 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