Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userThe semi-potent endomorphism ring of a module
حلقة الإندومورفيزمات شبه الجامدة لمودول
1036
1 58
0
(
0
)
Created by
Shamra Editor
Ask ChatGPT about the research
في هذه الورقة العلمية تمت دراسة مفهوم شبه جمودية حلقة الإندومورفيزمات لمودول ما. فضلا عن ذلك, تمت دراسة شبه جمودية حلقة الإندومورفيزمات للمودولات نصف الأفقية ( الإسقاطية ) المباشرة.
In this paper, we studied the concept of semi-potency of endomorphism ring of modules. In addition to that, it has been studied the endomorphism ring of semi injective ( projective) modules and direct injective ( projective) modules.
References used
Anderson F. W. & Fuller K. R: " Rings and categories of modules ", New York. Springer 1973
Goodearl K. R : " Von Neumann regular rings ", Pitman: 1979
Kasch F. Modules and rings, London Math. Soc. Mono.1982
rate research
Read More
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
.
In this scientific paper we dealt with three different types of
homomorphisms between two given ideals in a ring with unity shown as
follows: ring homomorphism, R- module homomorphism and ideal
homomorphism, which were supported by several example
s.
Furthermore, we prove that the family of ideals in a ring R with ring, R -
module and ideal homomorphisms forms the category of ideals of the first,
second and third type, respectively. The next step was dedicated to support all
previous ideals by examples and functor between such categories.
Any right R-module M is called a CS-module if every submodule of M is
essential in a direct summand of M. A ring is said to be CS-ring if R as a right
R-module is CS [9]. In this paper we study semiperfect ring in which each
simple right R-module
is essential in a direct summand of R. We call such ring
as a extending for simple R-module. Here we find that for such rings, every
simple R-module is weakly-injective if and only if R is weakly-injective if and
only if R is self-injective if and only if R is weakly-semisimple. Examples are
constructed for which simple R-module is essential in a direct summand.
Let R be a ring with identity.
The ain is to study some fundamental properties of a ring R when R is regular
or semi-potent and the radical Jacobson of R when R is semi-potent.
New results were obtained including necessary and sufficient condition
s of R
to be regular or semi-potent. New substructures of R are studied and their
relationship with the total of R.
It's considered that، the ring of linear operator of vector
space and stilled as a source of many mathematicians in general and
algebreians particularly in introducing a new concepts in algebra
and ring theory. In this subject I. Kaplansky proved
the following
theorem: "The ring of linear operators of finite dimension vector
space is regular".
The object of this paper is studying of ring of linear operator
of vector space in abstract algebra point of view.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
