Cotilting modules and homological ring epimorphisms

JOURNAL OF ALGEBRA

卷:441

Article

Bazzoni, Silvana

关键词: Cotilting modules;    Homological ring epimorphism;    Valuation domains;   

DOI  :  10.1016/j.jalgebra.2015.07.008

来源: Elsevier

【 摘 要 】

We show that every injective homological ring epimorphism f: R -> S where S-R has flat dimension at most one gives rise to a 1-cotilting R-module and we give sufficient conditions under which the converse holds true. Specializing to the case of a valuation domain R, we illustrate a bijective correspondence between equivalence classes of injective homological ring epimorphisms originating in R and cotilting classes of certain type and, in turn, a bijection with a class of smashing localizing subcategories of the derived category of R. Moreover, we obtain that every cotilting class over a valuation domain is a Tor-orthogonal class, hence it is of cocountable type even though in general cotilting classes are not of cofinite type. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free