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 ...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.展开更多
We introduce the concept of weak silting modules,which is a generalization of both silting modules and Tor-tilting modules.It is shown that W is a weak silting module if and only if its character module W+is cosilting...We introduce the concept of weak silting modules,which is a generalization of both silting modules and Tor-tilting modules.It is shown that W is a weak silting module if and only if its character module W+is cosilting.Some properties of weak silting modules are given.展开更多
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)。
文摘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.
基金supported in part by the National Natural Science Foundation of China(Grant No.11771202).
文摘We introduce the concept of weak silting modules,which is a generalization of both silting modules and Tor-tilting modules.It is shown that W is a weak silting module if and only if its character module W+is cosilting.Some properties of weak silting modules are given.
