ليكن N, M مودولين فوق الحلقة R . إن الغاية من هذه الورقة هو متابعة دراسة البنـى الجزئيـة
مثل الأساس و المثالي المنفرد و المثالي المنفرد الثنوي و التوتـال. نتـائج R للمودول (N , M (hom
جديدة تم الحصول عليها فعلى سبيل المثال تم إيجاد الشرط اللازم و الكافي كي يكون التوتال لحلقـة مـا
يساوي مثالياً معيناً لهذه الحلقة.
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
conditions the total of a ring R to equal some ideal of R.
References used
A. N. Abyzov: (2008), "Weakly regular modules over normal rings"; Siberain Math. J. V.49, N.4, 575-586
G. Azumaya: (1991), " F − Semi-perfect modules "; J. Algebra, 136, p.73-85
H. Hamza: (1998), " − 0 I Rings and − 0 I modules"; Math. J. Okayama Univ. Vol.40, p.91-97
In this research, we study right (left) dual semipotent rings as right
(left) rings, and dual semipotent modules as modules.
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
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.
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