Minimal silting modules and ring extensions  

作　　者：Lidia Angeleri Hügel Weiqing Cao 

机构地区：[1]Dipartimento di Informatica,Universitàdegli Studi di Verona,Verona I-37134,Italy [2]School of Mathematics and Statistics,Jiangsu Normal University,Xuzhou 221116,China

出　　处：《Science China Mathematics》2022年第9期1775-1794,共20页中国科学：数学（英文版）

基　　金：supported by Fondazione Cariverona,Program“Ricerca Scientifica di Eccellenza 2018”(Project“Reducing Complexity in Algebra,Logic,Combinatorics-REDCOM”);supported by China Scholarship Council(Grant No.201906860022)。

摘　　要：Ring epimorphisms often induce silting modules and cosilting modules,termed minimal silting or minimal cosilting.The aim of this paper is twofold.Firstly,we determine the minimal tilting and minimal cotilting modules over a tame hereditary algebra.In particular,we show that a large cotilting module is minimal if and only if it has an adic module as a direct summand.Secondly,we discuss the behavior of minimality under ring extensions.We show that minimal cosilting modules over a commutative noetherian ring extend to minimal cosilting modules along any flat ring epimorphism.Similar results are obtained for commutative rings of small homological dimensions.

关 键 词：minimal silting modules ring epimorphisms ring extensions minimal cosilting modules tame hereditary algebras 

分 类 号：O153.3[理学—数学]