INJECTIVE COVERS OVER COMMUTATIVE NOETHERIAN RINGS OF GLOBAL DIMENSION AT MOST TWO II KIM, HAE-SIK; SONG, YEONG-MOO;
In studying injective covers, the modules C such that Hom(E, C) = 0 and (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 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 -preenvelope.
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