Endoregular modules

We study modules whose endomorphism rings possess various forms of von Neumann regularity. We characterize these “regularity” properties for several classes of modules, including completely decomposable modules and finitely presented modules over commutative rings. We generalize many of the classic...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Anderson, D.D. [verfasserIn] Juett, J.R. [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2020

Schlagwörter:	Endomorphism ring Von Neumann regular ring (One-sided) unit-regular ring Strongly regular ring

Übergeordnetes Werk:	Enthalten in: Journal of pure and applied algebra - Amsterdam [u.a.] : North-Holland, Elsevier Science, 1971, 225
Übergeordnetes Werk:	volume:225

DOI / URN:	10.1016/j.jpaa.2020.106475

Katalog-ID:	ELV004430581

Internformat


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520			\|a We study modules whose endomorphism rings possess various forms of von Neumann regularity. We characterize these “regularity” properties for several classes of modules, including completely decomposable modules and finitely presented modules over commutative rings. We generalize many of the classic results about abelian groups with regular endomorphism rings to modules over one-dimensional commutative rings with Noetherian spectrum. To facilitate this study, we define a module M over a commutative ring R to be weakly endoregular if xM and ( 0 : M ( x ) ) are direct summands of M for each x ∈ R . We give several characterizations of weak endoregularity for various classes of modules.
650		4	\|a Endomorphism ring
650		4	\|a Von Neumann regular ring
650		4	\|a (One-sided) unit-regular ring
650		4	\|a Strongly regular ring
700	1		\|a Juett, J.R. \|e verfasserin \|4 aut
773	0	8	\|i Enthalten in \|t Journal of pure and applied algebra \|d Amsterdam [u.a.] : North-Holland, Elsevier Science, 1971 \|g 225 \|h Online-Ressource \|w (DE-627)266014445 \|w (DE-600)1466510-4 \|w (DE-576)074959654 \|x 1873-1376 \|7 nnns
773	1	8	\|g volume:225
912			\|a GBV_USEFLAG_U
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912			\|a GBV_ILN_22
912			\|a GBV_ILN_23
912			\|a GBV_ILN_24
912			\|a GBV_ILN_31
912			\|a GBV_ILN_32
912			\|a GBV_ILN_39
912			\|a GBV_ILN_40
912			\|a GBV_ILN_60
912			\|a GBV_ILN_62
912			\|a GBV_ILN_63
912			\|a GBV_ILN_65
912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
912			\|a GBV_ILN_74
912			\|a GBV_ILN_90
912			\|a GBV_ILN_95
912			\|a GBV_ILN_100
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2056
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2065
912			\|a GBV_ILN_2068
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2113
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2147
912			\|a GBV_ILN_2148
912			\|a GBV_ILN_2152
912			\|a GBV_ILN_2153
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_2522
912			\|a GBV_ILN_4012
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4126
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4249
912			\|a GBV_ILN_4251
912			\|a GBV_ILN_4305
912			\|a GBV_ILN_4306
912			\|a GBV_ILN_4307
912			\|a GBV_ILN_4313
912			\|a GBV_ILN_4322
912			\|a GBV_ILN_4323
912			\|a GBV_ILN_4324
912			\|a GBV_ILN_4325
912			\|a GBV_ILN_4326
912			\|a GBV_ILN_4333
912			\|a GBV_ILN_4334
912			\|a GBV_ILN_4335
912			\|a GBV_ILN_4338
912			\|a GBV_ILN_4367
912			\|a GBV_ILN_4393
912			\|a GBV_ILN_4700
936	b	k	\|a 31.20 \|j Algebra: Allgemeines
951			\|a AR
952			\|d 225

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author_variant	d a da j j jj
matchkey_str	article:18731376:2020----::noeuam
hierarchy_sort_str	2020
bklnumber	31.20
publishDate	2020
allfields	10.1016/j.jpaa.2020.106475 doi (DE-627)ELV004430581 (ELSEVIER)S0022-4049(20)30176-6 DE-627 ger DE-627 rda eng 510 DE-600 31.20 bkl Anderson, D.D. verfasserin aut Endoregular modules 2020 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We study modules whose endomorphism rings possess various forms of von Neumann regularity. We characterize these “regularity” properties for several classes of modules, including completely decomposable modules and finitely presented modules over commutative rings. We generalize many of the classic results about abelian groups with regular endomorphism rings to modules over one-dimensional commutative rings with Noetherian spectrum. To facilitate this study, we define a module M over a commutative ring R to be weakly endoregular if xM and ( 0 : M ( x ) ) are direct summands of M for each x ∈ R . We give several characterizations of weak endoregularity for various classes of modules. Endomorphism ring Von Neumann regular ring (One-sided) unit-regular ring Strongly regular ring Juett, J.R. verfasserin aut Enthalten in Journal of pure and applied algebra Amsterdam [u.a.] : North-Holland, Elsevier Science, 1971 225 Online-Ressource (DE-627)266014445 (DE-600)1466510-4 (DE-576)074959654 1873-1376 nnns volume:225 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT 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_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.20 Algebra: Allgemeines AR 225
spelling	10.1016/j.jpaa.2020.106475 doi (DE-627)ELV004430581 (ELSEVIER)S0022-4049(20)30176-6 DE-627 ger DE-627 rda eng 510 DE-600 31.20 bkl Anderson, D.D. verfasserin aut Endoregular modules 2020 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We study modules whose endomorphism rings possess various forms of von Neumann regularity. We characterize these “regularity” properties for several classes of modules, including completely decomposable modules and finitely presented modules over commutative rings. We generalize many of the classic results about abelian groups with regular endomorphism rings to modules over one-dimensional commutative rings with Noetherian spectrum. To facilitate this study, we define a module M over a commutative ring R to be weakly endoregular if xM and ( 0 : M ( x ) ) are direct summands of M for each x ∈ R . We give several characterizations of weak endoregularity for various classes of modules. Endomorphism ring Von Neumann regular ring (One-sided) unit-regular ring Strongly regular ring Juett, J.R. verfasserin aut Enthalten in Journal of pure and applied algebra Amsterdam [u.a.] : North-Holland, Elsevier Science, 1971 225 Online-Ressource (DE-627)266014445 (DE-600)1466510-4 (DE-576)074959654 1873-1376 nnns volume:225 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT 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_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.20 Algebra: Allgemeines AR 225
allfields_unstemmed	10.1016/j.jpaa.2020.106475 doi (DE-627)ELV004430581 (ELSEVIER)S0022-4049(20)30176-6 DE-627 ger DE-627 rda eng 510 DE-600 31.20 bkl Anderson, D.D. verfasserin aut Endoregular modules 2020 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We study modules whose endomorphism rings possess various forms of von Neumann regularity. We characterize these “regularity” properties for several classes of modules, including completely decomposable modules and finitely presented modules over commutative rings. We generalize many of the classic results about abelian groups with regular endomorphism rings to modules over one-dimensional commutative rings with Noetherian spectrum. To facilitate this study, we define a module M over a commutative ring R to be weakly endoregular if xM and ( 0 : M ( x ) ) are direct summands of M for each x ∈ R . We give several characterizations of weak endoregularity for various classes of modules. Endomorphism ring Von Neumann regular ring (One-sided) unit-regular ring Strongly regular ring Juett, J.R. verfasserin aut Enthalten in Journal of pure and applied algebra Amsterdam [u.a.] : North-Holland, Elsevier Science, 1971 225 Online-Ressource (DE-627)266014445 (DE-600)1466510-4 (DE-576)074959654 1873-1376 nnns volume:225 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT 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_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.20 Algebra: Allgemeines AR 225
allfieldsGer	10.1016/j.jpaa.2020.106475 doi (DE-627)ELV004430581 (ELSEVIER)S0022-4049(20)30176-6 DE-627 ger DE-627 rda eng 510 DE-600 31.20 bkl Anderson, D.D. verfasserin aut Endoregular modules 2020 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We study modules whose endomorphism rings possess various forms of von Neumann regularity. We characterize these “regularity” properties for several classes of modules, including completely decomposable modules and finitely presented modules over commutative rings. We generalize many of the classic results about abelian groups with regular endomorphism rings to modules over one-dimensional commutative rings with Noetherian spectrum. To facilitate this study, we define a module M over a commutative ring R to be weakly endoregular if xM and ( 0 : M ( x ) ) are direct summands of M for each x ∈ R . We give several characterizations of weak endoregularity for various classes of modules. Endomorphism ring Von Neumann regular ring (One-sided) unit-regular ring Strongly regular ring Juett, J.R. verfasserin aut Enthalten in Journal of pure and applied algebra Amsterdam [u.a.] : North-Holland, Elsevier Science, 1971 225 Online-Ressource (DE-627)266014445 (DE-600)1466510-4 (DE-576)074959654 1873-1376 nnns volume:225 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT 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_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.20 Algebra: Allgemeines AR 225
allfieldsSound	10.1016/j.jpaa.2020.106475 doi (DE-627)ELV004430581 (ELSEVIER)S0022-4049(20)30176-6 DE-627 ger DE-627 rda eng 510 DE-600 31.20 bkl Anderson, D.D. verfasserin aut Endoregular modules 2020 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We study modules whose endomorphism rings possess various forms of von Neumann regularity. We characterize these “regularity” properties for several classes of modules, including completely decomposable modules and finitely presented modules over commutative rings. We generalize many of the classic results about abelian groups with regular endomorphism rings to modules over one-dimensional commutative rings with Noetherian spectrum. To facilitate this study, we define a module M over a commutative ring R to be weakly endoregular if xM and ( 0 : M ( x ) ) are direct summands of M for each x ∈ R . We give several characterizations of weak endoregularity for various classes of modules. Endomorphism ring Von Neumann regular ring (One-sided) unit-regular ring Strongly regular ring Juett, J.R. verfasserin aut Enthalten in Journal of pure and applied algebra Amsterdam [u.a.] : North-Holland, Elsevier Science, 1971 225 Online-Ressource (DE-627)266014445 (DE-600)1466510-4 (DE-576)074959654 1873-1376 nnns volume:225 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT 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_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.20 Algebra: Allgemeines AR 225
language	English
source	Enthalten in Journal of pure and applied algebra 225 volume:225
sourceStr	Enthalten in Journal of pure and applied algebra 225 volume:225
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bklname	Algebra: Allgemeines
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topic_facet	Endomorphism ring Von Neumann regular ring (One-sided) unit-regular ring Strongly regular ring
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container_title	Journal of pure and applied algebra
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topic_title	510 DE-600 31.20 bkl Endoregular modules Endomorphism ring Von Neumann regular ring (One-sided) unit-regular ring Strongly regular ring
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title	Endoregular modules
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title_full	Endoregular modules
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title_auth	Endoregular modules
abstract	We study modules whose endomorphism rings possess various forms of von Neumann regularity. We characterize these “regularity” properties for several classes of modules, including completely decomposable modules and finitely presented modules over commutative rings. We generalize many of the classic results about abelian groups with regular endomorphism rings to modules over one-dimensional commutative rings with Noetherian spectrum. To facilitate this study, we define a module M over a commutative ring R to be weakly endoregular if xM and ( 0 : M ( x ) ) are direct summands of M for each x ∈ R . We give several characterizations of weak endoregularity for various classes of modules.
abstractGer	We study modules whose endomorphism rings possess various forms of von Neumann regularity. We characterize these “regularity” properties for several classes of modules, including completely decomposable modules and finitely presented modules over commutative rings. We generalize many of the classic results about abelian groups with regular endomorphism rings to modules over one-dimensional commutative rings with Noetherian spectrum. To facilitate this study, we define a module M over a commutative ring R to be weakly endoregular if xM and ( 0 : M ( x ) ) are direct summands of M for each x ∈ R . We give several characterizations of weak endoregularity for various classes of modules.
abstract_unstemmed	We study modules whose endomorphism rings possess various forms of von Neumann regularity. We characterize these “regularity” properties for several classes of modules, including completely decomposable modules and finitely presented modules over commutative rings. We generalize many of the classic results about abelian groups with regular endomorphism rings to modules over one-dimensional commutative rings with Noetherian spectrum. To facilitate this study, we define a module M over a commutative ring R to be weakly endoregular if xM and ( 0 : M ( x ) ) are direct summands of M for each x ∈ R . We give several characterizations of weak endoregularity for various classes of modules.
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title_short	Endoregular modules
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