{"title":"The reduction number of stretched ideals","authors":"K. Ozeki","doi":"10.2969/jmsj/86498649","DOIUrl":null,"url":null,"abstract":"The homological property of the associated graded ring of an ideal is an important problem in commutative algebra and algebraic geometry. In this paper we explore the almost Cohen-Macaulayness of the associated graded ring of stretched m-primary ideals in the case where the reduction number attains almost minimal value in a Cohen-Macaulay local ring (A,m). As an application, we present complete descriptions of the associated graded ring of stretched m-primary ideals with small reduction number.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2021-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Mathematical Society of Japan","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2969/jmsj/86498649","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
The homological property of the associated graded ring of an ideal is an important problem in commutative algebra and algebraic geometry. In this paper we explore the almost Cohen-Macaulayness of the associated graded ring of stretched m-primary ideals in the case where the reduction number attains almost minimal value in a Cohen-Macaulay local ring (A,m). As an application, we present complete descriptions of the associated graded ring of stretched m-primary ideals with small reduction number.
期刊介绍：
The Journal of the Mathematical Society of Japan (JMSJ) was founded in 1948 and is published quarterly by the Mathematical Society of Japan (MSJ). It covers a wide range of pure mathematics. To maintain high standards, research articles in the journal are selected by the editorial board with the aid of distinguished international referees. Electronic access to the articles is offered through Project Euclid and J-STAGE. We provide free access to back issues three years after publication (available also at Online Index).
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