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Register a new userRegular and Semipotent Rings
الحلقات المنتظمة و شبه الجامدة
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Damascus University ورقة بحثية
Publication date
2014
fields
Mathematics
and research's language is
العربية
Authors
حمزة حاكمي( باحث )
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Shamra Editor
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لتكن R حلقة واحدية. الهدف من هذه الورقة هو دراسة بعض الخواص الأساسية للحلقة R عندما تكون الحلقة R منتظمة أو شبه جامدة, و دراسة أساس جاكبسون للحلقة R تكون الحلقة R شبه جامدة. تم الحصول على نتائج جديدة تتضمن عدداً من الشروط اللازمة و الكافية كي تكون الحلقة R منتظمة أو شبه جامدة. و درست بنى جزئية جديدة في الحلقة R فضلاً عن دراسة علاقة هذه البنى الجزئية بالتوتال للحلقة 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 conditions of R to be regular or semi-potent. New substructures of R are studied and their relationship with the total of R.
References used
Kasch. F: (1982). Modules and Rings. Academic Press
Kasch. F, Mader. A. (2004). Rings, Modules, and the Total. Front. Math., Birkhauser Verlag, Basel
Nicholson. W. K. (1975). I-Rings. Trans. Amer. Math. Soc.207, p.361-373
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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.
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 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 .
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.
أساس جاكبسون
الحلقات شبه الجامدة
Jacobson radical
Endomorphism rings
حلقة الإندومورفيزمات لمودول
المودولات نصف الإسقاطية ( الأفقية )
المودولات الأفقية ( الإسقاطية ) المباشرة
المودولات المنتظمة
Semi-potent rings
Semi injective ( projective) Modules
Regular modules
( Direct projective injective ( projective
المزيد..
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