TITLE

On the existence of nonzero injective covers and projective envelopes of modules

AUTHOR(S)
Xiaoxiang ZHANG; Xianmei SONG
PUB. DATE
November 2013
SOURCE
Turkish Journal of Mathematics;Nov2013, Vol. 37 Issue 6, p914
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
In general, the injective cover (projective envelope) of a simple module can be zero. A ring R is called a weakly left V-ring (strongly left Kasch ring) if every simple left R-module has a nonzero injective cover (projective envelope). It is proven that every nonzero left R-module has a nonzero injective cover if and only if R is a left Artinian weakly left V-ring. Dually, every nonzero left R-module has a nonzero projective envelope if and only if R is a left perfect right coherent strongly left Kasch ring. Some related rings and examples are considered.
ACCESSION #
91512844

 

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