Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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INJECTIVE COVERS OVER COMMUTATIVE NOETHERIAN RINGS OF GLOBAL DIMENSION AT MOST TWO II

  • KIM, HAE-SIK (Department of Mathematics Kyungpook National University) ;
  • SONG, YEONG-MOO (Department of Mathematics Education Sunchon National University)
  • Published : 2005.07.01

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.

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References

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