A commutativity theorem for left s-unital rings
In this paper we generalize some well-known commutativity theorems for associative rings as follows: Let R be a left s-unital ring. If there exist nonnegative integers m>1, k≥0, and n≥0 such that for any x, y in R, [xky−xnym,x]=0, then R is commutative.
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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 |
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| Online Access: | http://dx.doi.org/10.1155/S0161171290001065 |
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| _version_ | 1832565077612429312 |
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| author | Hamza A. S. Abujabal |
| author_facet | Hamza A. S. Abujabal |
| author_sort | Hamza A. S. Abujabal |
| collection | DOAJ |
| description | In this paper we generalize some well-known commutativity theorems for associative rings as follows: Let R be a left s-unital ring. If there exist nonnegative integers m>1, k≥0, and n≥0 such that for any x, y in R, [xky−xnym,x]=0, then R is commutative. |
| format | Article |
| id | doaj-art-1a5d0ad71046402da5d53998da2cb7dc |
| 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-1a5d0ad71046402da5d53998da2cb7dc2025-02-03T01:09:14ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251990-01-0113476977410.1155/S0161171290001065A commutativity theorem for left s-unital ringsHamza A. S. Abujabal0Department of Mathematics, Faculty of Science, King Abdul-Aziz University, P.O. BOX 9028, Jeddah 21413, Saudi ArabiaIn this paper we generalize some well-known commutativity theorems for associative rings as follows: Let R be a left s-unital ring. If there exist nonnegative integers m>1, k≥0, and n≥0 such that for any x, y in R, [xky−xnym,x]=0, then R is commutative.http://dx.doi.org/10.1155/S0161171290001065associative rings-unital ringring with unitycommutativity of rings. |
| spellingShingle | Hamza A. S. Abujabal A commutativity theorem for left s-unital rings International Journal of Mathematics and Mathematical Sciences associative ring s-unital ring ring with unity commutativity of rings. |
| title | A commutativity theorem for left s-unital rings |
| title_full | A commutativity theorem for left s-unital rings |
| title_fullStr | A commutativity theorem for left s-unital rings |
| title_full_unstemmed | A commutativity theorem for left s-unital rings |
| title_short | A commutativity theorem for left s-unital rings |
| title_sort | commutativity theorem for left s unital rings |
| topic | associative ring s-unital ring ring with unity commutativity of rings. |
| url | http://dx.doi.org/10.1155/S0161171290001065 |
| work_keys_str_mv | AT hamzaasabujabal acommutativitytheoremforleftsunitalrings AT hamzaasabujabal commutativitytheoremforleftsunitalrings |