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: | , |
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| Format: | Article |
| Language: | English |
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Wiley
1990-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171290000126 |
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| _version_ | 1849415447587323904 |
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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. |
| format | Article |
| id | doaj-art-69093265ac2b47578d750fa2e32bddd6 |
| 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 |