On Commutative FGS-Rings
Let R be a ring. An R-module M is said to satisfy property (S) if every surjective endomorphism of M is an automorphism. Let F R be the class of finitely generated R-module and S R be the class of R-module satisfying property (S). In 1969 W. V. Vasconcelos proved that for every commutative ring R, F...
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| Published in | Communications in algebra Vol. 32; no. 5; pp. 1715 - 1727 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Taylor & Francis Group
31.12.2004
|
| Subjects | |
| Online Access | Get full text |
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| Abstract | Let R be a ring. An R-module M is said to satisfy property (S) if every surjective endomorphism of M is an automorphism. Let F
R
be the class of finitely generated R-module and S
R
be the class of R-module satisfying property (S). In 1969 W. V. Vasconcelos proved that for every commutative ring R, F
R
⊆ S
R
. In general this inclusion is strict. In this note we characterize commutative ring R for which F
R
= S
R
. |
|---|---|
| AbstractList | Let R be a ring. An R-module M is said to satisfy property (S) if every surjective endomorphism of M is an automorphism. Let F
R
be the class of finitely generated R-module and S
R
be the class of R-module satisfying property (S). In 1969 W. V. Vasconcelos proved that for every commutative ring R, F
R
⊆ S
R
. In general this inclusion is strict. In this note we characterize commutative ring R for which F
R
= S
R
. |
| Author | Sanghare, Mamadou Gueye, Cheikh Thiécoumba |
| Author_xml | – sequence: 1 givenname: Cheikh Thiécoumba surname: Gueye fullname: Gueye, Cheikh Thiécoumba email: cthgueye@netcourrier.com organization: Departement de Mathématiques et Informatique , Faculté des Sciences et Techniques, Université Cheikh Anta Diop – sequence: 2 givenname: Mamadou surname: Sanghare fullname: Sanghare, Mamadou organization: Departement de Mathématiques et Informatique , Faculté des Sciences et Techniques, Université Cheikh Anta Diop |
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| CitedBy_id | crossref_primary_10_1016_j_jalgebra_2006_07_010 |
| Cites_doi | 10.1090/S0002-9947-1969-0238839-5 |
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| Copyright | Copyright Taylor & Francis Group, LLC 2004 |
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| DOI | 10.1081/AGB-120029898 |
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| References | Vasconcelos W. V. (CIT0002) 1969; 138 CIT0001 |
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| Snippet | Let R be a ring. An R-module M is said to satisfy property (S) if every surjective endomorphism of M is an automorphism. Let F
R
be the class of finitely... |
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| StartPage | 1715 |
| SubjectTerms | FGS-ring Finitely generated module Principal ideal ring |
| Title | On Commutative FGS-Rings |
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