Document Type |
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Article In Journal |
Document Title |
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Commutativity of rings with variable constraints Commutativity of rings with variable constraints |
Document Language |
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Arabic |
Abstract |
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Let m > 1, r greater than or equal to 0 be fixed non-negative integers and R a ring with unity 1 in which for each x is an element of R, there exists a polynomial f(X,Y) = f(x)(X,Y) in R(X, Y) satisfying the condition that for all y in R f(x, y) = f(x, y + 1) = f(x, x + y) so that either of the properties y(r)[x, y(m)] = f(x, y) or [x, y(m)]y(r) = f(x, y) for all y in R. The main result of the present paper asserts that R is commutative if it satisfies the property Q(m) (for all x, y is an element of R, m[x, y] = 0 implies [x, y] = 0). Finally, some results have been extended to one-sided s-unital rings. |
Journal Name |
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PUBLICATIONES MATHEMATICAE-DEBRECEN |
Volume |
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58 |
Issue Number |
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3 |
Publishing Year |
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2001 AH
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Added Date |
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Tuesday, June 24, 2008 |
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Researchers
Khan MA | Khan MA | Researcher | | |
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