{"title":"Nagel-Schenzel公式的初等证明","authors":"A. Vahidi","doi":"10.29252/AS.2019.1359","DOIUrl":null,"url":null,"abstract":"Let R be a commutative Noetherian ring with non-zero identity, a an ideal of R, M a finitely generated R–module, and a1, . . . , an an a–filter regular M–sequence. The formula Ha(M) ∼= H i (a1,...,an) (M) for all i < n, Hi−n a (H n (a1,...,an) (M)) for all i ≥ n, is known as Nagel-Schenzel formula and is a useful result to express the local cohomology modules in terms of filter regular sequences. In this paper, we provide an elementary proof to this formula.","PeriodicalId":36596,"journal":{"name":"Algebraic Structures and their Applications","volume":"94 18","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"An elementary proof of Nagel-Schenzel formula\",\"authors\":\"A. Vahidi\",\"doi\":\"10.29252/AS.2019.1359\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let R be a commutative Noetherian ring with non-zero identity, a an ideal of R, M a finitely generated R–module, and a1, . . . , an an a–filter regular M–sequence. The formula Ha(M) ∼= H i (a1,...,an) (M) for all i < n, Hi−n a (H n (a1,...,an) (M)) for all i ≥ n, is known as Nagel-Schenzel formula and is a useful result to express the local cohomology modules in terms of filter regular sequences. In this paper, we provide an elementary proof to this formula.\",\"PeriodicalId\":36596,\"journal\":{\"name\":\"Algebraic Structures and their Applications\",\"volume\":\"94 18\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-03-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Algebraic Structures and their Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.29252/AS.2019.1359\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebraic Structures and their Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.29252/AS.2019.1359","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
摘要
设R是一个非零单位元的交换诺瑟环，a是R的理想，M是一个有限生成的R模，a1，…，一个a -滤波器正则m序列。公式Ha(M) ~ =Hi (a1，…，an) (M)对于所有i < n, Hi - n a(H n (a1，…，an) (M))对于所有i≥n，被称为Nagel-Schenzel公式，它是用滤波正则序列表示局部上同模的一个有用的结果。本文给出了这个公式的初等证明。
Let R be a commutative Noetherian ring with non-zero identity, a an ideal of R, M a finitely generated R–module, and a1, . . . , an an a–filter regular M–sequence. The formula Ha(M) ∼= H i (a1,...,an) (M) for all i < n, Hi−n a (H n (a1,...,an) (M)) for all i ≥ n, is known as Nagel-Schenzel formula and is a useful result to express the local cohomology modules in terms of filter regular sequences. In this paper, we provide an elementary proof to this formula.
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