### Abstract

Let R be a Gorenstein complete local ring. We say that finitely generated modules M and N are linked if Hom_{R/λR}(M,R/λR) ≅ Ω^{1}_{R/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 language | English |
---|---|

Pages (from-to) | 305-318 |

Number of pages | 14 |

Journal | Journal of Pure and Applied Algebra |

Volume | 149 |

Issue number | 3 |

Publication status | Published - Jun 6 2000 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Journal of Pure and Applied Algebra*,

*149*(3), 305-318.

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

Research output: Contribution to journal › Article

*Journal of Pure and Applied Algebra*, vol. 149, no. 3, pp. 305-318.

}

TY - JOUR

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

AU - Yoshino, Yuji

AU - Isogawa, Satoru

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.

UR - http://www.scopus.com/inward/record.url?scp=0034612180&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034612180&partnerID=8YFLogxK

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 -