{"title":"纤纤素心,简简单单","authors":"Lidia Angeleri Hügel, Ivo Herzog, Rosanna Laking","doi":"10.1007/s00209-024-03464-1","DOIUrl":null,"url":null,"abstract":"<p>Every cotilting module over a ring <i>R</i> induces a t-structure with a Grothendieck heart in the derived category D(Mod-<i>R</i>). We determine the simple objects in this heart and their injective envelopes, combining torsion-theoretic aspects with methods from the model theory of modules and Auslander-Reiten theory.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"25 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2024-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Simples in a cotilting heart\",\"authors\":\"Lidia Angeleri Hügel, Ivo Herzog, Rosanna Laking\",\"doi\":\"10.1007/s00209-024-03464-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Every cotilting module over a ring <i>R</i> induces a t-structure with a Grothendieck heart in the derived category D(Mod-<i>R</i>). We determine the simple objects in this heart and their injective envelopes, combining torsion-theoretic aspects with methods from the model theory of modules and Auslander-Reiten theory.</p>\",\"PeriodicalId\":18278,\"journal\":{\"name\":\"Mathematische Zeitschrift\",\"volume\":\"25 1\",\"pages\":\"\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-04-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematische Zeitschrift\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00209-024-03464-1\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematische Zeitschrift","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00209-024-03464-1","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
环 R 上的每一个同调模块都会在派生类 D(Mod-R) 中诱导出一个具有格罗内迪克心的 t 结构。我们结合扭转理论、模块模型理论和奥斯兰德-雷滕理论,确定了这个心的简单对象及其注入包络。
Every cotilting module over a ring R induces a t-structure with a Grothendieck heart in the derived category D(Mod-R). We determine the simple objects in this heart and their injective envelopes, combining torsion-theoretic aspects with methods from the model theory of modules and Auslander-Reiten theory.