# INJECTIVE COVERS OVER COMMUTATIVE NOETHERIAN RINGS OF GLOBAL DIMENSION AT MOST TWO II

KIM, HAE-SIK;SONG, YEONG-MOO

• Published : 2005.07.01
• 48 8

#### Abstract

In studying injective covers, the modules C such that Hom(E, C) = 0 and $Ext^1$(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 $\={D}$ of all direct summands of products of modules of finite length ([3, Theorem 2.9]). In this paper we show that every module over any commutative ring has a $\={D}$-preenvelope.

injective cover

#### References

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