The object of this paper is to study the relationship between certain projective modules and
their endomorphism rings. Specifically, the basic problem is to describe the projective …

If R is a simple ring with 1 which contains a maximal annihilator right ideal then R is the
endomorphism ring of a unital torsion-free module over an integral domain. We first prove …

R is called a left PS (resp. left min-coherent, left universally mininjective) ring if every simple
left ideal is projective (resp. finitely presented, a direct summand of R). We first investigate …

Throughout this paper, 𝑅is a commutative ring with identity and 𝑀 isan unitary R-module.
Aproper ideal 𝑃of a ring 𝑅 is primary if for all element 𝑎, 𝑏∈ 𝑅, 𝑎𝑏∈ 𝑃 implies either 𝑎∈ 𝑃 …

Let M, N be modules over a ring R and [M, N]= HomR (M, N). The concern is study of:(1)
Some fundamental properties of [M, N] when [M, N] is regular or semipotent.(2) The …

Camillo [31 and Faith [61 called a ring R a right max ring if every non-zero right R-module
has a maximal submodule. The class of right max rings includes right perfect rings (Bass [2]) …

For a ring R, there are classical facts that R is right Noetherian if and only if every direct sum
of injective right R-modules is injective, and R is right Noetherian if and only if every …

Let R be a Noetherian ring and let C be a semidualizing R-module. In this paper, by using
the classes 𝒫 C and ℐ C, we extend the notions of perfect and coperfect modules introduced …

The rings considered in this article are commutative with identity 1≠ 0 and the modules
considered in this article are modules over commutative rings and are unitary. We say that a …

MAXIMAL IDEALS OF THE ENDOMORPHISM RING OF AN INJECTIVE MODULE Page 1
Journal of Algebra and Its Applications Vol. 13, No. 4 (2014) 1350131 (21 pages) c© World …