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 …

A ring R is called left morphic, if for every a∈ R, R/Ra ࣅ 1 (a) where 1 (a) denotes the left
annihilator of a in R. The ring R is called strongly left morphic if every matrix ring Mn (R) is …

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 be a left module, over a ring R. M is called a Zelmanowitz-regular module if for each
x∊ M there exists a homomorphism f: M→ R such that f (x) x= x. Let Q be a left R-module and …

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 …

Let M be a left R-module. Then a proper submodule P of M is called weakly prime
submodule if for any ideals A and B of R and any submodule N of M such that ABN⊆ P, we …

Let R be a commutative ring with identity and M a unital R-module. The module M is said to
be a multiplication module provided for each submodule N of M there exists an ideal I of R …

In a recent paper, Aydoǧdu and López-Permouth have defined a module M to be N-
subinjective if every homomorphism N→ M extends to some E (N)→ M, where E (N) is the …

Let R be a ring with identity element and M be a unitary left R-module. M is called quasi-
injective if every element in Hom^ Af, M) for any R-module N in M is extened to an element in …

This paper is motivated by the results in [6]. We study some properties of strongly irreducible
submodules of a module. In fact, our objective is to investigate strongly irreducible modules …