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Document Type |
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Article In Journal |
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Document Title |
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Commutativity of rings through a Strebs result Commutativity of rings through a Strebs result |
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Document Language |
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Arabic |
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Abstract |
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In this paper we investigate commutativity of rings with unity satisfying any one of the properties:
{1 - g(gamma chi (m))} [gamma chi (m) - chi (T) f (gamma chi (m)) chi (s), ]{1 - h(gamma chi (m))} = 0, {1 - g(gamma chi (m))} [chi (m)gamma - chi (r) f (gamma chi (m))chi (s), chi]{1 - h(gamma chi (m))} = 0, gamma (t)[chi, gamma (n)] = g (chi)[f (chi), gamma ]h (chi) and [chi, gamma (n)] gamma (t) = g(chi)[f (chi)[f (chi), gamma ]h (chi)
for some f(X) in X(2)Z[X] and g(X), h(X) in Z[X], where m greater than or equal to 0, r greater than or equal to 0, s greater than or equal to 0, n > 0, t > 0 are non-negative integers. We also extend these results to the case when integral exponents in the underlying conditions are no longer fixed, rather they depend on the pair of ring elements chi and gamma far their values. Further, under different appropriate constraints on commutators, commutativity of rings has been studied. These results generalize a number of commutativity theorems established recently.
Document Type: Article
Language: English
Author Keywords: commutators; division rings; factorsubrings; polynomial identities; torsion-free rings
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Journal Name |
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CZECHOSLOVAK MATHEMATICAL JOURNAL |
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Volume |
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50 |
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Issue Number |
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4 |
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Publishing Year |
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2000 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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