{"title":"Tight closure of ideals on Witt rings","authors":"Shou Yoshikawa","doi":"arxiv-2409.06459","DOIUrl":null,"url":null,"abstract":"In this paper, we introduce the notions of tight closure of ideals on Witt\nrings and quasi-tightly closedness of system of parameters. By using the\nnotions, we obtain a characterization of quasi-$F$-rationality. Furthermore, we\nstudy the relationship between the closure operator and integrally closure.","PeriodicalId":501475,"journal":{"name":"arXiv - MATH - Commutative Algebra","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Commutative Algebra","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.06459","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we introduce the notions of tight closure of ideals on Witt
rings and quasi-tightly closedness of system of parameters. By using the
notions, we obtain a characterization of quasi-$F$-rationality. Furthermore, we
study the relationship between the closure operator and integrally closure.
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