Abstract Let R⊆ Q be rings such that the inclusion φ: R→ Q is an epimorphism in the
category of rings and Q is flat both as a right and as a left R-module. Assume that F. dim …

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 …

Let Λ be an artin algebra over a local commutative artinian ring k. We consider the category
P (Λ) whose objects are morphims f: P→ Q with P and Q projective left Λ-modules. In P (Λ) …

This paper introduces the notion of dual of automorphism extendable modules. A module M
is called automorphism-extendable if for every submodule N of M, every automorphism of N …

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) …

Let M and N be two modules. M is called automorphism N-invariant if for any essential
submodule A of N, any essential monomorphism f: A→ M can be extended to some g∈ Hom …

Let M be a left module over a ring R. A submodule N of M is called locally split in M if for
each x EN there exists a homomorphism h: Mt N such that h (x)= x. It is shown that if N is …

If R is a hereditary left artinian ring, then R is left pure semisimple if and only if the family R-
ind of all finitely generated indecomposable left R-modules has a (unique) Ext-injective …

All rings are assumed to be associative and to have a nonzero identity element. A ring is
said to be right (resp. left) invariant if all its right (resp. left) ideals are ideals. Expressions …

Let R and S be arbitrary rings, RM and SN countably generated free modules, and let φ: End
(RM)→ End (sN) be an isomorphism between the endomorphism rings of M and N. Camillo …