A note on symmetry in the vanishing of ext

Saeed Nasseh; Massoud Tousi

doi:10.1216/RMJ-2013-43-1-329

A note on symmetry in the vanishing of ext

Saeed Nasseh, Massoud Tousi

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

In [2] Avramov and Buchweitz proved that for finitely generated modules M and N over a complete intersection local ring R, Extⁱ _R(M,N) = 0 for all i ≫ 0 implies Extⁱ _R (N,M) = 0 for all i ≫ 0. In this note we give some generalizations of this result. Indeed we prove the abovementioned result when (1) M is finitely generated and N is arbitrary, (2) M is arbitrary and N has finite length and (3) M is complete and N is finitely generated.

Original language	English
Pages (from-to)	329-341
Number of pages	13
Journal	Rocky Mountain Journal of Mathematics
Volume	43
Issue number	1
DOIs	https://doi.org/10.1216/RMJ-2013-43-1-329
State	Published - 2013

Scopus Subject Areas

General Mathematics

Keywords

Complete intersection ring
Complete module
Gorenstein ring

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10.1216/RMJ-2013-43-1-329

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title = "A note on symmetry in the vanishing of ext",

abstract = "In [2] Avramov and Buchweitz proved that for finitely generated modules M and N over a complete intersection local ring R, Exti R(M,N) = 0 for all i ≫ 0 implies Exti R (N,M) = 0 for all i ≫ 0. In this note we give some generalizations of this result. Indeed we prove the abovementioned result when (1) M is finitely generated and N is arbitrary, (2) M is arbitrary and N has finite length and (3) M is complete and N is finitely generated.",

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AB - In [2] Avramov and Buchweitz proved that for finitely generated modules M and N over a complete intersection local ring R, Exti R(M,N) = 0 for all i ≫ 0 implies Exti R (N,M) = 0 for all i ≫ 0. In this note we give some generalizations of this result. Indeed we prove the abovementioned result when (1) M is finitely generated and N is arbitrary, (2) M is arbitrary and N has finite length and (3) M is complete and N is finitely generated.

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KW - Gorenstein ring

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JO - Rocky Mountain Journal of Mathematics

JF - Rocky Mountain Journal of Mathematics

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A note on symmetry in the vanishing of ext

Abstract

Scopus Subject Areas

Keywords

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