Linkage of Cohen-Macaulay modules over a gorenstein ring

Yuji Yoshino, Satoru Isogawa

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

Let R be a Gorenstein complete local ring. We say that finitely generated modules M and N are linked if HomR/λR(M,R/λR) ≅ Ω1R/λR(N), where λ is a regular sequence contained in both of the annihilators of M and N. We shall show that the Cohen-Macaulay approximation functor gives rise to a map Φr from the set of even linkage classes of Cohen-Macaulay modules of codimension r to the set of isomorphism classes of maximal Cohen-Macaulay modules. When r - 1, we give a condition for two modules to have the same image under the map Φr. If r - 2 and if R is a normal domain of dimension two, then we can show that Φr is a surjective map if and only if R is a unique factorization domain. Several explicit computations for hypersurface rings are also given.

Original languageEnglish
Pages (from-to)305-318
Number of pages14
JournalJournal of Pure and Applied Algebra
Volume149
Issue number3
Publication statusPublished - Jun 6 2000
Externally publishedYes

Fingerprint

Cohen-Macaulay Module
Gorenstein Ring
Linkage
Unique factorisation domain
Regular Sequence
Module
Annihilator
Isomorphism Classes
Cohen-Macaulay
Gorenstein
Local Ring
Functor
Codimension
Finitely Generated
Hypersurface
Two Dimensions
If and only if
Ring
Approximation

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Linkage of Cohen-Macaulay modules over a gorenstein ring. / Yoshino, Yuji; Isogawa, Satoru.

In: Journal of Pure and Applied Algebra, Vol. 149, No. 3, 06.06.2000, p. 305-318.

Research output: Contribution to journalArticle

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