{"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":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":"56 1","pages":"737-743"},"PeriodicalIF":0.6000,"publicationDate":"2016-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Kyungpook Mathematical Journal","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":"Q3","JCRName":"MATHEMATICS","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)。
期刊介绍：
Kyungpook Mathematical Journal is an international journal devoted to significant research concerning all aspects of mathematics. The journal has a preference for papers having a broad interest. One volume of the journal is published every year. Each volume until volume 42 consisted of two issues; however, starting from volume 43(2003), each volume consists of four issues. Authors should strive for expository clarity and good literary style. Manuscripts should be prepared as follows. The first page must consist of a short descriptive title, followed by the name(s) and address(es) of the author(s) along with an electronic address if available.
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