Turkish Journal of Mathematics
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.
DOI
10.3906/mat-1203-24
Keywords
Injective cover, projective envelope, weakly V-ring, strongly Kasch ring
First Page
914
Last Page
924
Recommended Citation
ZHANG, XIAOXIANG and SONG, XIANMEI
(2013)
"On the existence of nonzero injective covers and projective envelopes of modules,"
Turkish Journal of Mathematics: Vol. 37:
No.
6, Article 3.
https://doi.org/10.3906/mat-1203-24
Available at:
https://journals.tubitak.gov.tr/math/vol37/iss6/3
