精确的子类别、子函子和一些应用程序

Pub Date : 2023-09-27 DOI:10.1017/nmj.2023.29

HAILONG DAO, SOUVIK DEY, MONALISA DUTTA

{"title":"精确的子类别、子函子和一些应用程序","authors":"HAILONG DAO, SOUVIK DEY, MONALISA DUTTA","doi":"10.1017/nmj.2023.29","DOIUrl":null,"url":null,"abstract":"Abstract Let $({\\cal{A}},{\\cal{E}})$ be an exact category. We establish basic results that allow one to identify sub(bi)functors of ${\\operatorname{Ext}}_{\\cal{E}}(-,-)$ using additivity of numerical functions and restriction to subcategories. We also study a small number of these new functors over commutative local rings in detail and find a range of applications from detecting regularity to understanding Ulrich modules.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"EXACT SUBCATEGORIES, SUBFUNCTORS OF , AND SOME APPLICATIONS\",\"authors\":\"HAILONG DAO, SOUVIK DEY, MONALISA DUTTA\",\"doi\":\"10.1017/nmj.2023.29\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract Let $({\\\\cal{A}},{\\\\cal{E}})$ be an exact category. We establish basic results that allow one to identify sub(bi)functors of ${\\\\operatorname{Ext}}_{\\\\cal{E}}(-,-)$ using additivity of numerical functions and restriction to subcategories. We also study a small number of these new functors over commutative local rings in detail and find a range of applications from detecting regularity to understanding Ulrich modules.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2023-09-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1017/nmj.2023.29\",\"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":"1085","ListUrlMain":"https://doi.org/10.1017/nmj.2023.29","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 2

摘要

摘要设$({\cal{A}}，{\cal{E}})$是一个精确范畴。利用数值函数的可加性和对子范畴的限制，建立了可以识别${\operatorname{Ext}}_{\cal{E}}(-，-)$的子(bi)函子的基本结果。我们还详细研究了交换局部环上的少量这些新函子，并发现了从检测正则性到理解Ulrich模的一系列应用。

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

EXACT SUBCATEGORIES, SUBFUNCTORS OF , AND SOME APPLICATIONS

Abstract Let $({\cal{A}},{\cal{E}})$ be an exact category. We establish basic results that allow one to identify sub(bi)functors of ${\operatorname{Ext}}_{\cal{E}}(-,-)$ using additivity of numerical functions and restriction to subcategories. We also study a small number of these new functors over commutative local rings in detail and find a range of applications from detecting regularity to understanding Ulrich modules.

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