{"title":"A Generalization of Formal Local Cohomology Modules","authors":"S. Rezaei","doi":"10.5666/KMJ.2016.56.3.737","DOIUrl":null,"url":null,"abstract":". Let a and b be two ideals of a commutative Noetherian ring R , M a (cid:12)nitely generated R -module and i an integer. In this paper we study formal local cohomology modules with respect to a pair of ideals. We denote the i -th a -formal local cohomology module M with respect to b by F i a ; b ( M ). We show that if F i a ; b ( M ) is artinian, then a (cid:18) √ (0 : F i a ; b ( M )). Also, we show that F dim M a ; b ( M ) is artinian and we determine the set Att R F dim M a ; b ( M ).","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2016-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5666/KMJ.2016.56.3.737","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
. Let a and b be two ideals of a commutative Noetherian ring R , M a (cid:12)nitely generated R -module and i an integer. In this paper we study formal local cohomology modules with respect to a pair of ideals. We denote the i -th a -formal local cohomology module M with respect to b by F i a ; b ( M ). We show that if F i a ; b ( M ) is artinian, then a (cid:18) √ (0 : F i a ; b ( M )). Also, we show that F dim M a ; b ( M ) is artinian and we determine the set Att R F dim M a ; b ( M ).
． 设a和b是交换诺瑟环R的两个理想，M a (cid:12)完全生成R -模，i为整数。本文研究了关于一对理想的形式局部上同模。我们用F i a表示关于b的i - a -形式局部上同模M;b (M)。我们证明如果F i a;b (M)是人工的，那么a (cid:18)√(0:F ia;b (M))。我们还证明了F dim M;b (M)是人工的，我们确定集合Att R F dim M a;b (M)。
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