Let $ R $ be a ring. A morphism $\alpha: X\rightarrow Y $ of left $ R $-modules is called a
finitely phantom morphism if for each morphism ${\beta: F\rightarrow X} $ with $ F $ finitely …

A morphism f: M→ N of left R-modules is called an n-phantom morphism if the induced
morphism Tor n R (A, f)= 0 for every (finitely presented) right R-module A. Analogously, a …

A morphism f: M→ N of left R-modules is called a phantom morphism if the induced
morphism for every (finitely presented) right R-module A. Similarly, a morphism g: M→ N of …

Let R be a ring, Let A, C be left R-modules and f: A-+ C an epimorphism. f is called pure if
Hom (M, f): Hom.(M, A)-+ Hom,(M, C) is an epimorphism for all finitely presented left R …

A ring extension is a ring homomorphism preserving identities. In this paper, we give the
definition of relatively free modules on ring extensions and develop some basic properties of …

Let cp be a ring homomorphism from a ring R to a ring Q. If Q is flat as a right R-module and
q is a ring epimorphism, we say that QR is a flat epimorphism. If Q is projective with respect …

EPIMORPHISMS OF MODULES WHICH MUST BE ISOMORPHISMS Page 1 Canad. Math.
Bull. Vol. 16 (4), 1973 EPIMORPHISMS OF MODULES WHICH MUST BE ISOMORPHISMS BY …

In the previous no. te [7], we characterized" weakly" M-projective modules over a left PF ring.
In the present note, we study another type of" weakly" M-projective modules with a finiteness …

A module is called locally pure-projective if every pure epimor-phism onto it is locally split.
We prove that every locally pure-projective module is a Mittag-Leffler module. We derive …

A morphism f of left R-modules is called an RD-phantom morphism if the induced morphism
Tor1 (R= aR, f)= 0 for any a R. Similarly, a morphism g of left R-modules is said to be an …