Let M and N be right R-modules. Hom (M, N) is called regular if for each f∈ Hom (M, N),
there exists g∈ Hom (N, M) such that f= fgf. Let [M, N]= Hom R (M, N). We prove that if M is …

Let M and N be two modules over a ring R. The concern is about the four substructures of
hom R (M, N): the Jacobson radical J [M, N], the singular ideal Δ [M, N], the co-singular …

This paper contains new and known results on homomorphisms that are close to regular.
The main results are presented with proofs. All rings are assumed to be associative and with …

Abstract Let p: M→ N be a right minimal epimorphism. We prove that there exists a ring
isomorphism between two rings END RM (N)/J (END RM (N)) and END RN (M)/J (END RN …

Let R be a commutative ring, M an R-module and φ a be the endomorphism of M given by
right multiplication by a∈ R. We say that M is weakly-morphic if M/φ a (M)≅ ker (φ a) as R …

If M and N are modules, the concept of semiregularity (and regularity) of hom (M, N) is
defined and studied, and the connection with the relative direct injective-and direct …

A module M is called morphic if M/M α≅ ker (α) for all endomorphisms α in end (M), and a
ring R is called a left morphic ring if RR is a morphic module. We consider the open question …

An R-module M is called principally quasi-injective if each R-hornomorphism from a
principal submodule of M to M can be extended to an endomorphism of M. Many properties …

Modules Commuting (Via Hom) with Some Colimits Page 1 Czechoslovak Mathematical
Journal, 53 (128) (2003), 891–905 MODULES COMMUTING (VIA Hom) WITH SOME COLIMITS …

It is proved that if R is a right FBN ring then a non-zero right R-module M has the property
that HomR (M, N)≠ 0 for every non-zero submodule N of M if and only if HomR (M, R/P)≠ 0 …