Silting modules and ring epimorphisms

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• 作者：Lidia Angeleri Hü ; gel^a ; ^{lidia.angeleri@univr.it" class="auth_mail" title="E-mail the corresponding author} ; Frederik Marks^b ; ^{marks@mathematik.uni-stuttgart.de" class="auth_mail" title="E-mail the corresponding author} ; Jorge Vitó ; ria^a ; ¹ ; ^{jorge.vitoria@city.ac.uk" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Tilting module ; Silting module ; Ring epimorphism ; Universal localisation ; Torsion pair ; Hereditary ring
• 刊名：Advances in Mathematics
• 出版年：2016
• 出版时间：5 November 2016
• 年：2016
• 卷：303
• 期：Complete
• 页码：1044-1076
• 全文大小：583 K

文摘

There are well-known constructions relating ring epimorphisms and tilting modules. The new notion of silting module provides a wider framework for studying this interplay. To every partial silting module we associate a ring epimorphism which we describe explicitly as an idempotent quotient of the endomorphism ring of the Bongartz completion. For hereditary rings, this assignment is used to parametrise homological ring epimorphisms by silting modules. We further show that homological ring epimorphisms of a hereditary ring form a lattice which completes the poset of noncrossing partitions in the case of finite dimensional algebras.