JP Journal of Algebra, Number Theory and Applications
Volume 19, Issue 2, Pages 141 - 153
(December 2010)
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SOME PROPERTIES RELATED TO COMMUTATIVE WEAKLY FGI-RINGS
Mamadou Barry and Papa Cheikhou Diop
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Abstract: Let R be a
commutative ring with non-zero identity and M
be a unital R-module. Then M is called
weakly co-Hopfian if any injective endomorphism of M is essential. The ring R
is called weakly FGI-ring if any weakly co-Hopfian R-module is finitely generated. In this note, we show that a ring is
a weakly FGI-ring if and only if R is
an Artinian principal ideal ring. |
Keywords and phrases: FGI-ring, weakly FGI-ring, Artinian principal ideal ring, finitely generated module, co-Hopfian module, weakly co-Hopfian module. |
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