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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Bibliographic Details
Published inCommunications in algebra Vol. 32; no. 5; pp. 1715 - 1727
Main Authors Gueye, Cheikh Thiécoumba, Sanghare, Mamadou
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 31.12.2004
Subjects
FGS-ring
Finitely generated module
Principal ideal ring
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Summary: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 .
ISSN:0092-7872
1532-4125
DOI:10.1081/AGB-120029898