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Document Type |
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Article In Journal |
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Document Title |
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A COMMUTATIVITY STUDY FOR CERTAIN RINGS دراسة تبديليه لحلقات معينة |
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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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In this paper, we discuss with the polynomial identities of the form xs[x, y]xt yp[xn; ym]ryq = 0 and xs[x, y]xt + yp[xn, ym]ryq = 0, where s 0, t 0, n 0, p 0, q 0, r > 0 and m > 1 are fixed integers, and also they are different in the noncommutative situation. Firstly, it is shown that a semiprime ring is commutative if and only if it satisfies the above conditions. Secondly, commutativity of associative rings with unity 1 and without unit 1 have also been obtained if they satisfy above and related polynomial identities. Thirdly, the result for rings with unity 1 is extended to one-sided s-unital rings. Also, we give some examples that appreciate our results. Finally, we propose a problem for future endeavor. |
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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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56 |
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Issue Number |
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1 |
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Publishing Year |
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1431 AH
2010 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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