Abstract

We show that if R is a ring such that every nonzero left R-module has a nonzero injective cover, then R is left Artinian. The converse is not true. If R is commutative, then the properties are equivalent.

Department(s)

Mathematics

Document Type

Article

DOI

https://doi.org/10.35834/2001/1303163

Publication Date

2001

Recommended Citation

Belshoff, Richard, and Jinzhong Xu. "Nonzero injective covers of modules." Missouri Journal of Mathematical Sciences 13, no. 3 (2001): 163-171.

Journal Title

Missouri Journal of Mathematical Sciences

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