{"title":"维特环上理想的严密封闭","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":"{\"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}","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}
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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