On commutativity theorems for rings

Let R be an associative ring with unity. It is proved that if R satisfies the polynomial identity [xny−ymxn,x]=0(m>1,n≥1), then R is commutative. Two or more related results are also obtained.

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Main Authors: H. A. S. Abujabal, M. S. Khan
Format: Article
Language:English
Published: Wiley 1990-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Subjects:
Online Access:http://dx.doi.org/10.1155/S0161171290000126
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author H. A. S. Abujabal
M. S. Khan
author_facet H. A. S. Abujabal
M. S. Khan
author_sort H. A. S. Abujabal
collection DOAJ
description Let R be an associative ring with unity. It is proved that if R satisfies the polynomial identity [xny−ymxn,x]=0(m>1,n≥1), then R is commutative. Two or more related results are also obtained.
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institution Kabale University
issn 0161-1712
1687-0425
language English
publishDate 1990-01-01
publisher Wiley
record_format Article
series International Journal of Mathematics and Mathematical Sciences
spelling doaj-art-69093265ac2b47578d750fa2e32bddd62025-08-20T03:33:32ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251990-01-01131879210.1155/S0161171290000126On commutativity theorems for ringsH. A. S. Abujabal0M. S. Khan1Department of Mathematics, Faculty of Science, King Abdul Aziz University, P.O. BOX 9028, Jeddah 21413, Saudi ArabiaDepartment of Mathematics, Faculty of Science, King Abdul Aziz University, P.O. BOX 9028, Jeddah 21413, Saudi ArabiaLet R be an associative ring with unity. It is proved that if R satisfies the polynomial identity [xny−ymxn,x]=0(m>1,n≥1), then R is commutative. Two or more related results are also obtained.http://dx.doi.org/10.1155/S0161171290000126commutative ringstorsion free ringscenter of a ringcommutator ideal.
spellingShingle H. A. S. Abujabal
M. S. Khan
On commutativity theorems for rings
International Journal of Mathematics and Mathematical Sciences
commutative rings
torsion free rings
center of a ring
commutator ideal.
title On commutativity theorems for rings
title_full On commutativity theorems for rings
title_fullStr On commutativity theorems for rings
title_full_unstemmed On commutativity theorems for rings
title_short On commutativity theorems for rings
title_sort on commutativity theorems for rings
topic commutative rings
torsion free rings
center of a ring
commutator ideal.
url http://dx.doi.org/10.1155/S0161171290000126
work_keys_str_mv AT hasabujabal oncommutativitytheoremsforrings
AT mskhan oncommutativitytheoremsforrings