JP Journal of Algebra, Number Theory and Applications
Volume 31, Issue 1, Pages 31 - 37
(November 2013)
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ON COMMUTATIVE SEMI-FGI-RINGS
Mamadou Barry, Abdou Diouf and Ernest Bazubwabo
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Abstract: Let R be a ring. An R-module M is called semi-co-Hopfian if any injective endomorphism of M has a direct summand image. Let R be a commutative ring with be the class of finitely generatedR-modules; be the class of co-Hopfian R-modules and be the class of semi-co-Hopfian R-modules.
We have and in [8] Vasconcelos proved that if R is a commutative ring whose all prime ideals are maximal, then hence
In this article, we characterize commutative rings R on which a module M is semi-co-Hopfian if and only if M is finitely generated, i.e., |
Keywords and phrases: semi-FGI-ring, principal ideal ring, finitely generated module, finitely annihilated module, semi-co-Hopfian module, co-Hopfian module. |
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