A note on additively completely regular seminearrings

Abstract In the endeavour of obtaining semigroup theoretic analogues i.e., the analogues of structure theorems of completely regular semigroups in the setting of additively regular seminearrings we could obtain some results in Mukherjee et al. (Commun Algebra 45(12):5111–5122, 2017). But we could no...
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Autor*in:	Mukherjee, Rajlaxmi [verfasserIn] Manna, Tuhin Pal, Pavel

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2018

Schlagwörter:	Left (right) completely regular seminearring Generalized left (right) completely regular seminearring Union of near-rings (zero-symmetric near-rings)

Anmerkung:	© Springer Science+Business Media, LLC, part of Springer Nature 2018

Übergeordnetes Werk:	Enthalten in: Semigroup forum - New York, NY : Springer, 1970, 100(2018), 1 vom: 19. Nov., Seite 339-347
Übergeordnetes Werk:	volume:100 ; year:2018 ; number:1 ; day:19 ; month:11 ; pages:339-347

Links:	Volltext

DOI / URN:	10.1007/s00233-018-9983-9

Katalog-ID:	SPR002810409

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520			\|a Abstract In the endeavour of obtaining semigroup theoretic analogues i.e., the analogues of structure theorems of completely regular semigroups in the setting of additively regular seminearrings we could obtain some results in Mukherjee et al. (Commun Algebra 45(12):5111–5122, 2017). But we could not obtain the analogue of (i) ‘A semigroup is Clifford if and only if it is strong semilattice of groups’ and (ii) ‘ A semigroup is completely regular if and only if it is a union of groups’. In Mukherjee et al. (Commun Algebra, 10.1080/00927872.2018.1524011) we could obtain the analogue of (i) for some restricted type of left (right) Clifford seminearrings. The main purpose of this paper is to complete the remaining task i.e., to obtain the analogue of (ii) for a class of additively completely regular seminearrings. In order to accomplish this we have characterized those seminearrings which are union of near-rings (zero-symmetric near-rings) in the class of additively completely regular seminearrings.
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allfields	10.1007/s00233-018-9983-9 doi (DE-627)SPR002810409 (SPR)s00233-018-9983-9-e DE-627 ger DE-627 rakwb eng Mukherjee, Rajlaxmi verfasserin aut A note on additively completely regular seminearrings 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract In the endeavour of obtaining semigroup theoretic analogues i.e., the analogues of structure theorems of completely regular semigroups in the setting of additively regular seminearrings we could obtain some results in Mukherjee et al. (Commun Algebra 45(12):5111–5122, 2017). But we could not obtain the analogue of (i) ‘A semigroup is Clifford if and only if it is strong semilattice of groups’ and (ii) ‘ A semigroup is completely regular if and only if it is a union of groups’. In Mukherjee et al. (Commun Algebra, 10.1080/00927872.2018.1524011) we could obtain the analogue of (i) for some restricted type of left (right) Clifford seminearrings. The main purpose of this paper is to complete the remaining task i.e., to obtain the analogue of (ii) for a class of additively completely regular seminearrings. In order to accomplish this we have characterized those seminearrings which are union of near-rings (zero-symmetric near-rings) in the class of additively completely regular seminearrings. Left (right) completely regular seminearring (dpeaa)DE-He213 Generalized left (right) completely regular seminearring (dpeaa)DE-He213 Union of near-rings (zero-symmetric near-rings) (dpeaa)DE-He213 Manna, Tuhin aut Pal, Pavel aut Enthalten in Semigroup forum New York, NY : Springer, 1970 100(2018), 1 vom: 19. Nov., Seite 339-347 (DE-627)300187009 (DE-600)1481770-6 1432-2137 nnns volume:100 year:2018 number:1 day:19 month:11 pages:339-347 https://dx.doi.org/10.1007/s00233-018-9983-9 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_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_120 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_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_2188 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_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 100 2018 1 19 11 339-347
spelling	10.1007/s00233-018-9983-9 doi (DE-627)SPR002810409 (SPR)s00233-018-9983-9-e DE-627 ger DE-627 rakwb eng Mukherjee, Rajlaxmi verfasserin aut A note on additively completely regular seminearrings 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract In the endeavour of obtaining semigroup theoretic analogues i.e., the analogues of structure theorems of completely regular semigroups in the setting of additively regular seminearrings we could obtain some results in Mukherjee et al. (Commun Algebra 45(12):5111–5122, 2017). But we could not obtain the analogue of (i) ‘A semigroup is Clifford if and only if it is strong semilattice of groups’ and (ii) ‘ A semigroup is completely regular if and only if it is a union of groups’. In Mukherjee et al. (Commun Algebra, 10.1080/00927872.2018.1524011) we could obtain the analogue of (i) for some restricted type of left (right) Clifford seminearrings. The main purpose of this paper is to complete the remaining task i.e., to obtain the analogue of (ii) for a class of additively completely regular seminearrings. In order to accomplish this we have characterized those seminearrings which are union of near-rings (zero-symmetric near-rings) in the class of additively completely regular seminearrings. Left (right) completely regular seminearring (dpeaa)DE-He213 Generalized left (right) completely regular seminearring (dpeaa)DE-He213 Union of near-rings (zero-symmetric near-rings) (dpeaa)DE-He213 Manna, Tuhin aut Pal, Pavel aut Enthalten in Semigroup forum New York, NY : Springer, 1970 100(2018), 1 vom: 19. Nov., Seite 339-347 (DE-627)300187009 (DE-600)1481770-6 1432-2137 nnns volume:100 year:2018 number:1 day:19 month:11 pages:339-347 https://dx.doi.org/10.1007/s00233-018-9983-9 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_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_120 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_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_2188 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_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 100 2018 1 19 11 339-347
allfields_unstemmed	10.1007/s00233-018-9983-9 doi (DE-627)SPR002810409 (SPR)s00233-018-9983-9-e DE-627 ger DE-627 rakwb eng Mukherjee, Rajlaxmi verfasserin aut A note on additively completely regular seminearrings 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract In the endeavour of obtaining semigroup theoretic analogues i.e., the analogues of structure theorems of completely regular semigroups in the setting of additively regular seminearrings we could obtain some results in Mukherjee et al. (Commun Algebra 45(12):5111–5122, 2017). But we could not obtain the analogue of (i) ‘A semigroup is Clifford if and only if it is strong semilattice of groups’ and (ii) ‘ A semigroup is completely regular if and only if it is a union of groups’. In Mukherjee et al. (Commun Algebra, 10.1080/00927872.2018.1524011) we could obtain the analogue of (i) for some restricted type of left (right) Clifford seminearrings. The main purpose of this paper is to complete the remaining task i.e., to obtain the analogue of (ii) for a class of additively completely regular seminearrings. In order to accomplish this we have characterized those seminearrings which are union of near-rings (zero-symmetric near-rings) in the class of additively completely regular seminearrings. Left (right) completely regular seminearring (dpeaa)DE-He213 Generalized left (right) completely regular seminearring (dpeaa)DE-He213 Union of near-rings (zero-symmetric near-rings) (dpeaa)DE-He213 Manna, Tuhin aut Pal, Pavel aut Enthalten in Semigroup forum New York, NY : Springer, 1970 100(2018), 1 vom: 19. Nov., Seite 339-347 (DE-627)300187009 (DE-600)1481770-6 1432-2137 nnns volume:100 year:2018 number:1 day:19 month:11 pages:339-347 https://dx.doi.org/10.1007/s00233-018-9983-9 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_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_120 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_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_2188 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_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 100 2018 1 19 11 339-347
allfieldsGer	10.1007/s00233-018-9983-9 doi (DE-627)SPR002810409 (SPR)s00233-018-9983-9-e DE-627 ger DE-627 rakwb eng Mukherjee, Rajlaxmi verfasserin aut A note on additively completely regular seminearrings 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract In the endeavour of obtaining semigroup theoretic analogues i.e., the analogues of structure theorems of completely regular semigroups in the setting of additively regular seminearrings we could obtain some results in Mukherjee et al. (Commun Algebra 45(12):5111–5122, 2017). But we could not obtain the analogue of (i) ‘A semigroup is Clifford if and only if it is strong semilattice of groups’ and (ii) ‘ A semigroup is completely regular if and only if it is a union of groups’. In Mukherjee et al. (Commun Algebra, 10.1080/00927872.2018.1524011) we could obtain the analogue of (i) for some restricted type of left (right) Clifford seminearrings. The main purpose of this paper is to complete the remaining task i.e., to obtain the analogue of (ii) for a class of additively completely regular seminearrings. In order to accomplish this we have characterized those seminearrings which are union of near-rings (zero-symmetric near-rings) in the class of additively completely regular seminearrings. Left (right) completely regular seminearring (dpeaa)DE-He213 Generalized left (right) completely regular seminearring (dpeaa)DE-He213 Union of near-rings (zero-symmetric near-rings) (dpeaa)DE-He213 Manna, Tuhin aut Pal, Pavel aut Enthalten in Semigroup forum New York, NY : Springer, 1970 100(2018), 1 vom: 19. Nov., Seite 339-347 (DE-627)300187009 (DE-600)1481770-6 1432-2137 nnns volume:100 year:2018 number:1 day:19 month:11 pages:339-347 https://dx.doi.org/10.1007/s00233-018-9983-9 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_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_120 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_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_2188 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_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 100 2018 1 19 11 339-347
allfieldsSound	10.1007/s00233-018-9983-9 doi (DE-627)SPR002810409 (SPR)s00233-018-9983-9-e DE-627 ger DE-627 rakwb eng Mukherjee, Rajlaxmi verfasserin aut A note on additively completely regular seminearrings 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract In the endeavour of obtaining semigroup theoretic analogues i.e., the analogues of structure theorems of completely regular semigroups in the setting of additively regular seminearrings we could obtain some results in Mukherjee et al. (Commun Algebra 45(12):5111–5122, 2017). But we could not obtain the analogue of (i) ‘A semigroup is Clifford if and only if it is strong semilattice of groups’ and (ii) ‘ A semigroup is completely regular if and only if it is a union of groups’. In Mukherjee et al. (Commun Algebra, 10.1080/00927872.2018.1524011) we could obtain the analogue of (i) for some restricted type of left (right) Clifford seminearrings. The main purpose of this paper is to complete the remaining task i.e., to obtain the analogue of (ii) for a class of additively completely regular seminearrings. In order to accomplish this we have characterized those seminearrings which are union of near-rings (zero-symmetric near-rings) in the class of additively completely regular seminearrings. Left (right) completely regular seminearring (dpeaa)DE-He213 Generalized left (right) completely regular seminearring (dpeaa)DE-He213 Union of near-rings (zero-symmetric near-rings) (dpeaa)DE-He213 Manna, Tuhin aut Pal, Pavel aut Enthalten in Semigroup forum New York, NY : Springer, 1970 100(2018), 1 vom: 19. Nov., Seite 339-347 (DE-627)300187009 (DE-600)1481770-6 1432-2137 nnns volume:100 year:2018 number:1 day:19 month:11 pages:339-347 https://dx.doi.org/10.1007/s00233-018-9983-9 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_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_120 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_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_2188 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_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 100 2018 1 19 11 339-347
language	English
source	Enthalten in Semigroup forum 100(2018), 1 vom: 19. Nov., Seite 339-347 volume:100 year:2018 number:1 day:19 month:11 pages:339-347
sourceStr	Enthalten in Semigroup forum 100(2018), 1 vom: 19. Nov., Seite 339-347 volume:100 year:2018 number:1 day:19 month:11 pages:339-347
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institution	findex.gbv.de
topic_facet	Left (right) completely regular seminearring Generalized left (right) completely regular seminearring Union of near-rings (zero-symmetric near-rings)
isfreeaccess_bool	false
container_title	Semigroup forum
authorswithroles_txt_mv	Mukherjee, Rajlaxmi @@aut@@ Manna, Tuhin @@aut@@ Pal, Pavel @@aut@@
publishDateDaySort_date	2018-11-19T00:00:00Z
hierarchy_top_id	300187009
id	SPR002810409
language_de	englisch
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author	Mukherjee, Rajlaxmi
spellingShingle	Mukherjee, Rajlaxmi misc Left (right) completely regular seminearring misc Generalized left (right) completely regular seminearring misc Union of near-rings (zero-symmetric near-rings) A note on additively completely regular seminearrings
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topic_title	A note on additively completely regular seminearrings Left (right) completely regular seminearring (dpeaa)DE-He213 Generalized left (right) completely regular seminearring (dpeaa)DE-He213 Union of near-rings (zero-symmetric near-rings) (dpeaa)DE-He213
topic	misc Left (right) completely regular seminearring misc Generalized left (right) completely regular seminearring misc Union of near-rings (zero-symmetric near-rings)
topic_unstemmed	misc Left (right) completely regular seminearring misc Generalized left (right) completely regular seminearring misc Union of near-rings (zero-symmetric near-rings)
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title	A note on additively completely regular seminearrings
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title_full	A note on additively completely regular seminearrings
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title_sort	note on additively completely regular seminearrings
title_auth	A note on additively completely regular seminearrings
abstract	Abstract In the endeavour of obtaining semigroup theoretic analogues i.e., the analogues of structure theorems of completely regular semigroups in the setting of additively regular seminearrings we could obtain some results in Mukherjee et al. (Commun Algebra 45(12):5111–5122, 2017). But we could not obtain the analogue of (i) ‘A semigroup is Clifford if and only if it is strong semilattice of groups’ and (ii) ‘ A semigroup is completely regular if and only if it is a union of groups’. In Mukherjee et al. (Commun Algebra, 10.1080/00927872.2018.1524011) we could obtain the analogue of (i) for some restricted type of left (right) Clifford seminearrings. The main purpose of this paper is to complete the remaining task i.e., to obtain the analogue of (ii) for a class of additively completely regular seminearrings. In order to accomplish this we have characterized those seminearrings which are union of near-rings (zero-symmetric near-rings) in the class of additively completely regular seminearrings. © Springer Science+Business Media, LLC, part of Springer Nature 2018
abstractGer	Abstract In the endeavour of obtaining semigroup theoretic analogues i.e., the analogues of structure theorems of completely regular semigroups in the setting of additively regular seminearrings we could obtain some results in Mukherjee et al. (Commun Algebra 45(12):5111–5122, 2017). But we could not obtain the analogue of (i) ‘A semigroup is Clifford if and only if it is strong semilattice of groups’ and (ii) ‘ A semigroup is completely regular if and only if it is a union of groups’. In Mukherjee et al. (Commun Algebra, 10.1080/00927872.2018.1524011) we could obtain the analogue of (i) for some restricted type of left (right) Clifford seminearrings. The main purpose of this paper is to complete the remaining task i.e., to obtain the analogue of (ii) for a class of additively completely regular seminearrings. In order to accomplish this we have characterized those seminearrings which are union of near-rings (zero-symmetric near-rings) in the class of additively completely regular seminearrings. © Springer Science+Business Media, LLC, part of Springer Nature 2018
abstract_unstemmed	Abstract In the endeavour of obtaining semigroup theoretic analogues i.e., the analogues of structure theorems of completely regular semigroups in the setting of additively regular seminearrings we could obtain some results in Mukherjee et al. (Commun Algebra 45(12):5111–5122, 2017). But we could not obtain the analogue of (i) ‘A semigroup is Clifford if and only if it is strong semilattice of groups’ and (ii) ‘ A semigroup is completely regular if and only if it is a union of groups’. In Mukherjee et al. (Commun Algebra, 10.1080/00927872.2018.1524011) we could obtain the analogue of (i) for some restricted type of left (right) Clifford seminearrings. The main purpose of this paper is to complete the remaining task i.e., to obtain the analogue of (ii) for a class of additively completely regular seminearrings. In order to accomplish this we have characterized those seminearrings which are union of near-rings (zero-symmetric near-rings) in the class of additively completely regular seminearrings. © Springer Science+Business Media, LLC, part of Springer Nature 2018
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title_short	A note on additively completely regular seminearrings
url	https://dx.doi.org/10.1007/s00233-018-9983-9
remote_bool	true
author2	Manna, Tuhin Pal, Pavel
author2Str	Manna, Tuhin Pal, Pavel
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doi_str	10.1007/s00233-018-9983-9
up_date	2024-07-03T15:20:52.199Z
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