Injective Covers Over Commutative Noetherian Rings of Global Dimension at most two II
Commun. Korean Math. Soc. 2005 Vol. 20, No. 3, 437-442 Printed September 1, 2005
Hae-Sik Kim, Yeong-Moo Song Kyungpook National University, Sunchon National University
Abstract : In studying injective covers, the modules $C$ such that $ \mbox{Hom} ( E,C ) = 0 $ and $ \mbox{Ext}^1 ( E,C ) = 0 $ for all injective module $E$ play an important role because of Wakamatsu's lemma. If $C$ is a module over the ring $ k [[ x,y ]] $ with $k$ a field, the class of these modules $C$ contains the class $\bar D$ of all direct summands of products of modules of finite length (\cite[Theorem 2.9]{eks}). In this paper we show that every module over any commutative ring has a $\bar D$-preenvelope.
