The object of this paper is to study the total as substructure of hom (M,N) R
for any two modules R M and R N , one of interesting question, is when the total
of a module N equals the hom (N, J (N)) R .
The object of this paper is to study the locally projective and locally injective
modules. Specifically, this paper is a continuation of study of locally projective
and locally injective modules, where a new description of locally projective and
locally injective modules is obtained.
The object of this paper is to study the endomorphism rings of locally
projective and locally injective modules. Specifically, this paper is a continuation
of study of endomorphism rings of locally projective and locally injective modules
to be semipotent rings.
Let M and N be two modules over a ring R. The object of this paper is the study
of substructures of hom (M, N) R such as, radical, the singular, and co-singular
ideal and the total. The new obtained results include necessary and sufficient
conditi
ons the total of a ring R to equal some ideal of R.
The objective of this paper is to continue our study for a right 1 I - rings and
to generalize the concept of 1 I - rings to modules. We call a ring R a right
1 I - ring if every right annihilator for any element of R contains a nonzero
idempotent
.
The objectiv of this paper is to study the relationship between certain ring R
and endomorphism rings of free modules over R. Specifically, the basic problem is
to describe ring R, which for it endomorphism ring of all free R-module, is a
generali
zed right Baer ring, right I1-ring.
Call a ring R is a generalized right Baer ring if any right annihilator contains
a non-zero idempotent. We call a ring R is right I1-ring if the right annihilator of
any element of R contains a non-zero idempotent. This text is showing that each
right ideal of a ring R contains a projective right ideal if the endomorphism ring
of any free R-module is a right I1-ring. And shown over a ring R, the
endomorphism ring of any free R-module is a generalized right Baer ring if and
only if endomorphism ring of any free R-module is an I1-ring.
The object of this paper is to study the relationship between certain ring R
and endomorphism rings of free modules over R. Specifically, the basic
problem is to describe ring R, which is endomorphism ring of all free Rmodule,
as a generalized rig
ht Bear ring. Call a ring R a generalized right Bear
ring if any right annihilator contains a nonzero idempotent. A structure
theorem is obtained: endomorphism ring of a free module F is a generalized
right Bear ring if and only if every closed submodule of F contains a direct
summand of F. It is shown that every torsionless R-module contains a
projective R-module if endomorphism ring of any free R-module is a
generalized right Bear ring.