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Register a new userQuasi–Hereditary Rings and Modules
الحلقات و المودولات شبه الوراثية
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إن مفهوم الحلقات و المودولات الوراثية و نصف الوراثية ذو أثر كبير في نظرية الحلقات و المودولات نظرا لارتباط هذا المفهوم بحلقات و مودولات بيير وريكارت. لهذا السبب قمنا بتعميم هذا المفهوم تحت اسم الحلقات و المودولات شبه الوراثية .
The concept of hereditary and semi-hereditary rings and modules has grate effect in Theory of rings and modules, because the relation between this concepts with Baer and Rickart rings and modules. For this reason, we generalize this concept by quasihereditary rings.
References used
Cartan H & Eilenberg S: " Homological algebra ", Princeton Univesity Press, Princeton 1956
(Lam T.Y: " A First Course in Non-Commutative Rings ", New -York Springer (2001
Rizvi S.T & Roman C.S: " On Direct Summand of Baer Modules ", J. Algebra, (2009), 321, (2), 682 – 696
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In this research, we study right (left) dual semipotent rings as right
(left) rings, and dual semipotent modules as modules.
Regular modules
الحلقة اليمينية (اليسارية) المرافقة لحلقة شبه جامدة
حلقة يمينية (يسارية)
المودول المرافق لمودول شبه جامد
حلقة يمينية (يسارية) رئيسية
right (left) dual semipotent rings
right (left) rings
dual semipotent modules
principal right (left) rings
retractable module
epi-retractable module
rickart modules
Injective module
المزيد..
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.
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.
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 purpose of this paper is studying some properties of clean,
semi-clean and quasi-clean rings, and study the relationship between
these rings. A ring is called clean if each of its element is the sum of
an idempotent and a unit, a ring is calle
d semi-clean if each of its
element is the sum of an idempotent and a regular, a ring is called
quasi-clean if each of its element is the sum of an idempotent and an
pi .
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