Covers induced by Ext

JOURNAL OF ALGEBRA

卷:231

Article

Eklof, PC ; Trlifaj, J

关键词: precover;    cover;    right approximation;    Ext;    Tor;    pure-injective module;    Dedekind domain;    axiom of constructibility;    flat cover conjecture;   

DOI  :  10.1006/jabr.2000.8343

来源: Elsevier

【 摘 要 】

We prove a generalization of the flat cover conjecture by showing for any ring R that (1) each (right R-) module has a Ker Ext(-, C)-cover, for any class of pure-injective modules C, and that (2) each module has a Ker Tor(-, B)-cover, for any class of left R-modules B. For Dedekind domains, we describe Ker Ext(-, 8) explicitly for any class of cotorsion modules C; in particular, we prove that (1) holds, and that Ker Ext(-, B) is a cotilting torsion-free class. For right hereditary rings, we prove the consistency of the existence of special Ker Ext(-, G)-precovers for any set of modules G. (C) 2000 Academic Press.

【 授权许可】

Free