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Document Type |
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Article In Journal |
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Document Title |
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CLASSIFICATION OF RINGS SATISFYING SOME CONSTRAINTS ON SUBSETS تصنيف حلقات تلبية بعض القيود على مجموعات فرعية |
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Subject |
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Algebra-Ring Theory |
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Document Language |
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English |
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Abstract |
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Abstract. Let R be an associative ring with identity 1 and J(R) the Jacob- son radical of R. Suppose that m _ 1 is a fixed positive integer and R an m-torsion-free ring with 1. In the present paper, it is shown that R is commu- tative if R satisfies both the conditions (i) [xm, ym] = 0 for all x, y 2 R\J(R) and (ii) [x, [x, ym]] = 0, for all x, y 2 R\J(R). This result is also valid if (ii) is replaced by (ii)’ [(yx)mxm − xm(xy)m, x] = 0, for all x, y 2 R\N(R). Our results generalize many well-known commutativity theorems (cf. [1], [2], [3], [4], [5], [6], [9], [10], [11] and [14]). |
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ISSN |
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1319-0989 |
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Journal Name |
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Arts and Humanities Journal |
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Volume |
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43 |
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Issue Number |
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1 |
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Publishing Year |
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1428 AH
2007 AD |
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Article Type |
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Article |
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Added Date |
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Wednesday, January 12, 2011 |
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Researchers
| محرم على خان | Khan, Moharram Ali | Researcher | Doctorate | mkhan91@gmail.com |
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