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Register a new userSemiperfect ring which is Extending for simple modules
الحلقة نصف التامة التي هي ممدد لمودول بسيط
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Added by
Damascus University ورقة بحثية
Publication date
2004
fields
Mathematics
and research's language is
العربية
Created by
Shamra Editor
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نقول عن المودول اليمين M فوق الحلقة R إنه CS – مودول إذا كان كل مـودول جزئـي مـن M أساسياً في مجموع مباشر لـ M . و نقول عن الحلقة R إنها CS – حلقة يمينية إذا كانت R كمودول يميني على نفسها هي CS –مودول (9) . في هذه المقالة ندرس الحلقات نصف التامة و التي من أجلها كل مودول يميني بـسيط هـو مـودول أساسي في مجموع مباشر لـ R . ندعو هذه الحلقات بأنها ممدد للمودول البسيط فوق R .و هنا نجد أنه من أجل هـذه الحلقـات كـل مودول بسيط فوق R هو أفقي بضعف عندما وفق عندما تكون الحلقة R مودولاً أفقي بضعف و هذا يكافئ أيضاً إن الحلقة R نصف بسيطة بضعف. و قد تم بناء أمثلة لمودولات بسيطة و التي من أجلها يكون المودول البسيط أساسياً في مجموع مباشر لها.
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.
References used
(F.W. ANDERSON and K.R. FULLER, “Rings and categories of modules”, Springer-Verlag, New York / Heidelberg / Berlin, (1974
(C.FAITH, “Alegebra :Rings, modules and categories I,”Springer-Verlag, New York / Heidelberg! Berlin, (1973
B.L. OSOFSKY, A Generalization of Quasi-Frobemous Ring, Journal fo Algebra 4 (1966), 373-387
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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
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