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- Title
Higher Phantom Morphisms with Respect to a Subfunctor of Ext.
- Authors
Mao, Lixin
- Abstract
A morphism f:M→N of left R-modules is called an n-phantom morphism (resp. a Torn-epimorphism) if the induced morphism Torn(A, f) = 0 (resp. Torn(A, f) is an epimorphism) for every (finitely presented) right R-module A. Analogously, a morphism g:X→Y of left R-modules is said to be an n-Ext-phantom morphism (resp. Extn-monomorphism) if the induced morphism Extn(B, g) = 0 (resp. Extn(B, g) is a monomorphism) for every finitely presented left R-module B. It is proven that a morphism f is an n-phantom morphism if and only if the pullback of any epimorphism along f is a Torn-epimorphism; A morphism g is an n-Ext-phantom morphism if and only if the pushout of any monomorphism along g is an Extn-monomorphism. We also prove that every module has an object-special n-phantom precover. In addition, we introduce and investigate n-phantomless and n-Ext-phantomless rings.
- Publication
Algebras & Representation Theory, 2019, Vol 22, Issue 2, p407
- ISSN
1386-923X
- Publication type
Academic Journal
- DOI
10.1007/s10468-018-9773-9