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Register a new userA study About Clean and Quasi- CleanRings
دراسة حول الحلقات النظيفة و شبه النظيفة
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Aِl-Baath University ورقة بحثية
Publication date
2015
fields
Mathematics
and research's language is
العربية
Authors
هناء كاظم( باحث )
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Shamra Editor
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يتعلق البحث بدراسة بعض الخواص للحلقات النظيفة و نصف النظيفة و شبه النظيفة و ايجاد العلاقة بين هذه الحلقات. نقول عن حلقة ما إنها نظيفة إذا كان كل عنصر فيها هو مجموع عنصرين أحدهما جامد و الآخر قابل للقلب, و نقول عن حلقة ما إنها نصف نظيفة إذا كان كل عنصر فيها هو مجموع عنصرين أحدهما جامد و الآخر منتظم, نقول عن حلقة ما إنها شبه نظيفة إذا كان كل عنصر فيها هو مجموع عنصرين أحدهما جامد و الآخر pi عنصر.
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 called 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 .
References used
Jacobson, N 1956 Structure of Rings. Amer. Math. Soc. Coll. Publ
Goodearl, K.R, 1979 Von Neumann Regular Rings. Pitman, London
Kasch, F 1982 Modules and Rings. Academic Press, New York, p. 372
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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.
In this paper, the characterization of right and left quasi-Frobenius
categories, has been given.
Let C be a small preadditive category, C* the dual category of C. It has
shown, that the following conditions are equivalent:
(i) C is right and lef
t quasi-Frobenius;
(ii) All flat C-modules and all flat C*-modules are injective;
(iii) All injective C-modules and all injective C*-modules are projective.
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.
In this paper, We study the dual representation. We proved that if
p is completely redusibile, decomposable and unitary then p* is
completely redusibile, decomposable and unitary,
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