Higher phantom morphisms with respect to a subfunctor of Ext
L Mao - Algebras and Representation Theory, 2019 - Springer
A morphism f: M→ N f:M→N of left R-modules is called an n-phantom morphism (resp. a Tor
n-epimorphism) if the induced morphism Tor n (A, f)= 0 (resp. Tor n (A, f) is an epimorphism)
for every (finitely presented) right R-module A. Analogously, a morphism g: X→ Y g:X→Y of
left R-modules is said to be an n-Ext-phantom morphism (resp. Ext n-monomorphism) if the
induced morphism Ext n (B, g)= 0 (resp. Ext n (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 …
n-epimorphism) if the induced morphism Tor n (A, f)= 0 (resp. Tor n (A, f) is an epimorphism)
for every (finitely presented) right R-module A. Analogously, a morphism g: X→ Y g:X→Y of
left R-modules is said to be an n-Ext-phantom morphism (resp. Ext n-monomorphism) if the
induced morphism Ext n (B, g)= 0 (resp. Ext n (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 …
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