上局部上同调模的共性与湮灭子

IF 0.2 4区数学 Q4 MATHEMATICS Mathematical Reports Pub Date : 2022-01-01 DOI:10.59277/mrar.2023.25.75.1.133

Iraj Bagheriyeh, K. Bahmanpour, G. Ghasemi

{"title":"上局部上同调模的共性与湮灭子","authors":"Iraj Bagheriyeh, K. Bahmanpour, G. Ghasemi","doi":"10.59277/mrar.2023.25.75.1.133","DOIUrl":null,"url":null,"abstract":"\"Let R be a Noetherian ring and I be an ideal of R. Let M be a finitely generated R-module with cd(I,M) = t ≥ 0 and assume that L is the largest submodule of M such that cd(I,L) < cd(I,M). It is shown that AnnR Ht I (M) = AnnRM/L in each of the following cases: (i) dimM/IM ≤ 1. (ii) dimR/I ≤ 1. (iii) The R-module Hi I (M) is Artinian for each i ≥ 2. (iv) The R-module Hi I (R) is Artinian for each i ≥ 2. (v) cd(I,M) ≤ 1. (vi) cd(I,R) ≤ 1. (vii) The Rmodule Ht I (M) is Artinian and I-cofinite. These assertions answer affirmatively a question raised by Atazadeh et al. in [2], in some special cases.\"","PeriodicalId":49858,"journal":{"name":"Mathematical Reports","volume":"37 1","pages":""},"PeriodicalIF":0.2000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"\\\"COFINITENESS AND ANNIHILATORS OF TOP LOCAL COHOMOLOGY MODULES\\\"\",\"authors\":\"Iraj Bagheriyeh, K. Bahmanpour, G. Ghasemi\",\"doi\":\"10.59277/mrar.2023.25.75.1.133\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"\\\"Let R be a Noetherian ring and I be an ideal of R. Let M be a finitely generated R-module with cd(I,M) = t ≥ 0 and assume that L is the largest submodule of M such that cd(I,L) < cd(I,M). It is shown that AnnR Ht I (M) = AnnRM/L in each of the following cases: (i) dimM/IM ≤ 1. (ii) dimR/I ≤ 1. (iii) The R-module Hi I (M) is Artinian for each i ≥ 2. (iv) The R-module Hi I (R) is Artinian for each i ≥ 2. (v) cd(I,M) ≤ 1. (vi) cd(I,R) ≤ 1. (vii) The Rmodule Ht I (M) is Artinian and I-cofinite. These assertions answer affirmatively a question raised by Atazadeh et al. in [2], in some special cases.\\\"\",\"PeriodicalId\":49858,\"journal\":{\"name\":\"Mathematical Reports\",\"volume\":\"37 1\",\"pages\":\"\"},\"PeriodicalIF\":0.2000,\"publicationDate\":\"2022-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Reports\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.59277/mrar.2023.25.75.1.133\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Reports","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.59277/mrar.2023.25.75.1.133","RegionNum":4,"RegionCategory":"数学","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noether环，I是R的一个理想，设M是一个有限生成的R模，cd(I,M) = t≥0，并设L是M的最大子模，使得cd(I,L) < cd(I,M)。可以看出，在以下情况下，AnnR Ht I (M) = AnnRM/L:(I) dimM/IM≤1。(ii) dimR/I≤1。(iii)当I≥2时，r模Hi I (M)为Artinian。(iv)当I≥2时，R模Hi I (R)为Artinian。(v) cd(I,M)≤1。(vi) cd(I,R)≤1。(vii) r模hti (M)是Artinian和I- finite。这些断言肯定地回答了Atazadeh等人在[2]中在某些特殊情况下提出的问题。”

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

"COFINITENESS AND ANNIHILATORS OF TOP LOCAL COHOMOLOGY MODULES"

"Let R be a Noetherian ring and I be an ideal of R. Let M be a finitely generated R-module with cd(I,M) = t ≥ 0 and assume that L is the largest submodule of M such that cd(I,L) < cd(I,M). It is shown that AnnR Ht I (M) = AnnRM/L in each of the following cases: (i) dimM/IM ≤ 1. (ii) dimR/I ≤ 1. (iii) The R-module Hi I (M) is Artinian for each i ≥ 2. (iv) The R-module Hi I (R) is Artinian for each i ≥ 2. (v) cd(I,M) ≤ 1. (vi) cd(I,R) ≤ 1. (vii) The Rmodule Ht I (M) is Artinian and I-cofinite. These assertions answer affirmatively a question raised by Atazadeh et al. in [2], in some special cases."

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Mathematical Reports MATHEMATICS-

CiteScore

0.20

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The journal MATHEMATICAL REPORTS (formerly STUDII SI CERCETARI MATEMATICE) was founded in 1948 by the Mathematics Section of the Romanian Academy. It appeared under its first name until 1998 and received the name of Mathematical Reports in 1999. It is now published in one volume a year, consisting in 4 issues. The current average total number of pages is 500. Our journal MATHEMATICAL REPORTS publishes original mathematical papers, written in English. Excellent survey articles may be also accepted. The editors will put strong emphasis on originality, quality and applicability.

期刊最新文献

SESQUILINEAR FORMS AND THE ORTHOGONALITY PRESERVING PROPERTY GAPS IN A SUMSET OF A POLYNOMIAL WITH ITSELF ARMENDARIZ MODULES AND NILTORSIONLESS MODULES HOMOLOGY THEORY OF MULTIPLICATIVE HOM-LIE ALGEBRAS SHORTER PROOF OF THE RIESZ INTERPOLATION FORMULA FOR TRIGONOMETRIC POLYNOMIALS