TY - JOUR

T1 - Linkage of Cohen-Macaulay modules over a gorenstein ring

AU - Yoshino, Yuji

AU - Isogawa, Satoru

N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.

PY - 2000/6/6

Y1 - 2000/6/6

N2 - 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.

AB - 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.

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U2 - 10.1016/S0022-4049(98)00167-4

DO - 10.1016/S0022-4049(98)00167-4

M3 - Article

AN - SCOPUS:0034612180

VL - 149

SP - 305

EP - 318

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

IS - 3

ER -