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I1 -RINGS

الـ I1 ـ حـلقـات

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 Publication date 2006
  fields Mathematics
and research's language is العربية
 Created by Shamra Editor




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The objectiv of this paper is to study the relationship between certain ring R and endomorphism rings of free modules over R. Specifically, the basic problem is to describe ring R, which for it endomorphism ring of all free R-module, is a generalized right Baer ring, right I1-ring. Call a ring R is a generalized right Baer ring if any right annihilator contains a non-zero idempotent. We call a ring R is right I1-ring if the right annihilator of any element of R contains a non-zero idempotent. This text is showing that each right ideal of a ring R contains a projective right ideal if the endomorphism ring of any free R-module is a right I1-ring. And shown over a ring R, the endomorphism ring of any free R-module is a generalized right Baer ring if and only if endomorphism ring of any free R-module is an I1-ring.

References used
Faith, C. (1981). Algebra, Rings, Modules and Categories, T.2, Springer - Verlag 190
Ôhori, M. (1984). On non-commutative generalized P.P. rings, Math.J. Okayama Univ. 26 , p.157-167
Hakmi, H. & Alshikh. M. (2005). Generalized Baer ring, Damascus University J. for the basic sciences. Vol.21,N.1,p.10-14
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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 relationship between certain ring R and endomorphism rings of free modules over R. Specifically, the basic problem is to describe ring R, which is endomorphism ring of all free Rmodule, as a generalized rig ht Bear ring. Call a ring R a generalized right Bear ring if any right annihilator contains a nonzero idempotent. A structure theorem is obtained: endomorphism ring of a free module F is a generalized right Bear ring if and only if every closed submodule of F contains a direct summand of F. It is shown that every torsionless R-module contains a projective R-module if endomorphism ring of any free R-module is a generalized right Bear ring.
The objective of this paper is to continue our study for a right 1 I - rings and to generalize the concept of 1 I - rings to modules. We call a ring R a right 1 I - ring if every right annihilator for any element of R contains a nonzero idempotent .
هذا بحث في اللغة يتناول ظاهرة البناء للمجهول في اللغة العربية، و قد تكون من مقدمة، و ثلاث قضايا أساسية هي: أهمية الفعل المبني للمجهول، و مصطلحاته، و أغراضه.

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