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 …

In [3], Bass has shown that a ring R is left perfect if and only if every flat left R-module is
projective and if and only if R satisfies the descending chain condition on principal right …

A family C of finitely generated indecomposable modules is said to have right almost split
morphisms if there is a right almost split morphism f: N→ M in add C for each …

Our concern is with modules M such that every homomorphism from a closed submodule of
M to M can be lifted to M. Although such modules share some of the properties of extending …

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 …

Proposition 1: a) M has SIP if and only if for every pair ofsummands S and T with TT: M+ S
the projection map, the kernel of the restricted map vIT is a summand. b) If M has SIP and S c …

Almost split sequences of modules were introduced and studied in the last three papers in
the series [1,..., 6] by Auslander and Reiten and, with the related simple functors and …

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 …

An important part of Clifford's theory does not work properly for arbitrary fields R. To see why,
we must recall the main steps of this theory. We are interested in extensions to RH-modules …

The paper deals with almost split sequences. Introduced in [2] for the category mod A of
finitely generated modules over an artin algebra A, almost split sequences were later found …