Courtney R. Gibbons, David A. Jorgensen, J. Striuli
{"title":"𝐿-dimension用于本地环上的模块","authors":"Courtney R. Gibbons, David A. Jorgensen, J. Striuli","doi":"10.1090/conm/773/15534","DOIUrl":null,"url":null,"abstract":"<p>We introduce a new homological dimension for finitely generated modules over a commutative local ring <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper R\"> <mml:semantics> <mml:mi>R</mml:mi> <mml:annotation encoding=\"application/x-tex\">R</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, which is based on a complex derived from a free resolution <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L\"> <mml:semantics> <mml:mi>L</mml:mi> <mml:annotation encoding=\"application/x-tex\">L</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of the residue field of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper R\"> <mml:semantics> <mml:mi>R</mml:mi> <mml:annotation encoding=\"application/x-tex\">R</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, and called <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L\"> <mml:semantics> <mml:mi>L</mml:mi> <mml:annotation encoding=\"application/x-tex\">L</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-dimension. We prove several properties of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L\"> <mml:semantics> <mml:mi>L</mml:mi> <mml:annotation encoding=\"application/x-tex\">L</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-dimension, give some applications, and compare <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L\"> <mml:semantics> <mml:mi>L</mml:mi> <mml:annotation encoding=\"application/x-tex\">L</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-dimension to complete intersection dimension.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"𝐿-dimension for modules over a local ring\",\"authors\":\"Courtney R. Gibbons, David A. Jorgensen, J. Striuli\",\"doi\":\"10.1090/conm/773/15534\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We introduce a new homological dimension for finitely generated modules over a commutative local ring <inline-formula content-type=\\\"math/mathml\\\"> <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper R\\\"> <mml:semantics> <mml:mi>R</mml:mi> <mml:annotation encoding=\\\"application/x-tex\\\">R</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, which is based on a complex derived from a free resolution <inline-formula content-type=\\\"math/mathml\\\"> <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper L\\\"> <mml:semantics> <mml:mi>L</mml:mi> <mml:annotation encoding=\\\"application/x-tex\\\">L</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of the residue field of <inline-formula content-type=\\\"math/mathml\\\"> <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper R\\\"> <mml:semantics> <mml:mi>R</mml:mi> <mml:annotation encoding=\\\"application/x-tex\\\">R</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, and called <inline-formula content-type=\\\"math/mathml\\\"> <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper L\\\"> <mml:semantics> <mml:mi>L</mml:mi> <mml:annotation encoding=\\\"application/x-tex\\\">L</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-dimension. We prove several properties of <inline-formula content-type=\\\"math/mathml\\\"> <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper L\\\"> <mml:semantics> <mml:mi>L</mml:mi> <mml:annotation encoding=\\\"application/x-tex\\\">L</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-dimension, give some applications, and compare <inline-formula content-type=\\\"math/mathml\\\"> <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper L\\\"> <mml:semantics> <mml:mi>L</mml:mi> <mml:annotation encoding=\\\"application/x-tex\\\">L</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-dimension to complete intersection dimension.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2021-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1090/conm/773/15534\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/conm/773/15534","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We introduce a new homological dimension for finitely generated modules over a commutative local ring RR, which is based on a complex derived from a free resolution LL of the residue field of RR, and called LL-dimension. We prove several properties of LL-dimension, give some applications, and compare LL-dimension to complete intersection dimension.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
