{"title":"ANNIHILATORS OF TOP LOCAL COHOMOLOGY MODULES DEFINED BY A PAIR OF IDEALS","authors":"S. Karimi, S. Payrovi","doi":"10.24330/IEJA.586962","DOIUrl":null,"url":null,"abstract":"Let $R$ be a commutative Noetherian ring, $I, J$ two proper ideals of $R$ and let $M$ be a non-zero finitely generated $R$-module with $c={\\rm cd}(I,J,M)$. In this paper, we first introduce $T_R(I,J,M)$ as the largest submodule of $M$ with the property that ${\\rm cd}(I,J,T_R(I,J,M))<c$ and we describe it in terms of the reduced primary decomposition of zero submodule of $M$. It is shown that ${\\rm Ann}_R(H_{I,J}^d(M))={\\rm Ann}_R(M/{T_R(I,J,M)})$ and ${\\rm Ann}_R(H_{I}^d(M))={\\rm Ann}_R(H_{I,J}^d(M))$, whenever $R$ is a local ring, $M$ has dimension $d$ with $H_{I,J}^d(M)\\\\\\neq0$ and $J^tM\\subseteq T_R(I,M)$ for some positive integer $t$.","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":" ","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2019-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Electronic Journal of Algebra","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.24330/IEJA.586962","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 3
Abstract
Let $R$ be a commutative Noetherian ring, $I, J$ two proper ideals of $R$ and let $M$ be a non-zero finitely generated $R$-module with $c={\rm cd}(I,J,M)$. In this paper, we first introduce $T_R(I,J,M)$ as the largest submodule of $M$ with the property that ${\rm cd}(I,J,T_R(I,J,M))
期刊介绍：
The International Electronic Journal of Algebra is published twice a year. IEJA is reviewed by Mathematical Reviews, MathSciNet, Zentralblatt MATH, Current Mathematical Publications. IEJA seeks previously unpublished papers that contain: Module theory Ring theory Group theory Algebras Comodules Corings Coalgebras Representation theory Number theory.
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