{"title":"A NOTE ON COHOMOLOGICAL DIMENSION OVER COHEN-MACAULAY RINGS","authors":"Iraj Bagheriyeh, K. Bahmanpour, G. Ghasemi","doi":"10.4134/BKMS.B190165","DOIUrl":null,"url":null,"abstract":"Let (R,m) be a Noetherian local Cohen-Macaulay ring and I be a proper ideal of R. Assume that βR(I, R) denotes the constant value of depthR(R/I n) for n 0. In this paper we introduce the new notion γR(I, R) and then we prove the following inequalities: βR(I, R) ≤ γR(I, R) ≤ dimR− cd(I, R) ≤ dimR/I. Also, some applications of these inequalities will be included.","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"57 1","pages":"275-280"},"PeriodicalIF":0.6000,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the Korean Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4134/BKMS.B190165","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Let (R,m) be a Noetherian local Cohen-Macaulay ring and I be a proper ideal of R. Assume that βR(I, R) denotes the constant value of depthR(R/I n) for n 0. In this paper we introduce the new notion γR(I, R) and then we prove the following inequalities: βR(I, R) ≤ γR(I, R) ≤ dimR− cd(I, R) ≤ dimR/I. Also, some applications of these inequalities will be included.
期刊介绍：
This journal endeavors to publish significant research of broad interests in pure and applied mathematics. One volume is published each year, and each volume consists of six issues (January, March, May, July, September, November).
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