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.
"Nonzero Injective Covers of Modules." Missouri J. Math. Sci. 13 (3) 163 - 171, Fall 2001. https://doi.org/10.35834/2001/1303163