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Register a new userGeneralized Right Bear Rings
حلقـات بيـر المعممـة
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موضوع هذا البحث هو دراسة العلاقة بين حلقة ماR و بين حلقة الإندومورفيزمات لمـودول حـرF، فوق هذه الحلقة. و بشكل خاص فقد تم وصف الحلقة التي تكون لأجلها حلقة الإندومورفيزمات لأي مودول حر فوقها، و هي حلقة بير المعممة. حيث تم إثبـات أن الـشرط الـلازم و الكـافي لكـي تكـون حلقـة الإندومورفيزمات لمودول حر حلقة بير هو أن يحوي كل مودول جزئي مغلق من هذا المودول الحر حـداً مباشراً. كذلك فقد تم إثبات أنه إذا كانت حلقة الاندومورفيزمات لمودول حر F حلقة بير المعممة, فإن كـل مودول جزئي دون فتل من F يحوي مودولاً إسقاطياً.
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 right 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.
References used
Kaplansky, I. (1968). Rings of Operator, New York: Amsterdam: W.A.Benjamin inc
Tsukerman, G. M. (1966). Rings of Endomorphisms of free module, Siberian. Math. J.7,923-927
(Goodearl, K. R. (1976). Ring Theory, Non-Singular Rings and modules, Pure and Appl. Math. N33, Dekker (new york
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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
generali
zed 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.
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 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
.
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ut perform poorly on the hard test set without superficial cues. Previous approaches have resorted to manual methods of encouraging models not to overfit to superficial cues. While some of the methods have improved performance on hard instances, they also lead to degraded performance on easy in- stances. Here, we propose to explicitly learn a model that does well on both the easy test set with superficial cues and the hard test set without superficial cues. Using a meta-learning objective, we learn such a model that improves performance on both the easy test set and the hard test set. By evaluating our models on Choice of Plausible Alternatives (COPA) and Commonsense Explanation, we show that our proposed method leads to improved performance on both the easy test set and the hard test set upon which we observe up to 16.5 percentage points improvement over the baseline.
The purpose of the research is to study the Bergman function and Bergman distance to generalize Moreau – Yosida Approximation.
To do that we replace the quadratic additive terms in Moreau – Yosida Approximates by more general Bergman distance and s
tudy properties of generalized approximation and prove equivalence between epigraph – convergence and pointwise convergence of the generalized Moreau – Yosida Approximation.
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