Document Type |
: |
Article In Journal |
Document Title |
: |
A COMMUTATIVITY STUDY FOR CERTAIN RINGS دراسة تبديليه لحلقات معينة |
Subject |
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Algebra-Ring Theory |
Document Language |
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English |
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. |
ISSN |
: |
1319-0989 |
Journal Name |
: |
Arts and Humanities Journal |
Volume |
: |
56 |
Issue Number |
: |
1 |
Publishing Year |
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1431 AH
2010 AD |
Article Type |
: |
Article |
Added Date |
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Saturday, January 1, 2011 |
|
Researchers
محرم علي خان | Khan, Moharram Ali | Investigator | Doctorate | mkhan91@gmail.com |
|