On center-like elements in rings
In a paper with a similar title Herstein has considered the structure of prime rings which contain an element a which satisfies either [a,x]n=0 or is in the center of R for each x in R. We consider the structure of rings which contain an element a which satisfies powers of certain higher commutators...
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| Format: | Article |
| Language: | English |
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Wiley
1985-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171285000138 |
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| _version_ | 1849402247506558976 |
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| author | Joe W. Fisher Mohamed H. Fahmy |
| author_facet | Joe W. Fisher Mohamed H. Fahmy |
| author_sort | Joe W. Fisher |
| collection | DOAJ |
| description | In a paper with a similar title Herstein has considered the structure of prime rings which contain an element a which satisfies either [a,x]n=0 or is in the center of R for each x in R. We consider the structure of rings which contain an element a which satisfies powers of certain higher commutators. The two types which we consider are (1) […[[a,x1],x2],…xm]n=0 or is in the center of R for all x1,x2,…,xm in R and (2) [a,[x1,[x2,…,[xm−1,xm]…]]]n for all x1,x2,…,xm in R. We obtain results similar to those obtained by Herstein; however, in some cases we must strengthen the hypotheses. |
| format | Article |
| id | doaj-art-8b04be4af7cd4b51b8206df6089b9a21 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1985-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-8b04be4af7cd4b51b8206df6089b9a212025-08-20T03:37:34ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251985-01-018114514910.1155/S0161171285000138On center-like elements in ringsJoe W. Fisher0Mohamed H. Fahmy1University of Cincinnati, Cincinnati 45221, Ohio, USAUniversity of Cincinnati, Cincinnati 45221, Ohio, USAIn a paper with a similar title Herstein has considered the structure of prime rings which contain an element a which satisfies either [a,x]n=0 or is in the center of R for each x in R. We consider the structure of rings which contain an element a which satisfies powers of certain higher commutators. The two types which we consider are (1) […[[a,x1],x2],…xm]n=0 or is in the center of R for all x1,x2,…,xm in R and (2) [a,[x1,[x2,…,[xm−1,xm]…]]]n for all x1,x2,…,xm in R. We obtain results similar to those obtained by Herstein; however, in some cases we must strengthen the hypotheses.http://dx.doi.org/10.1155/S0161171285000138prime and semiprime ringsprimitive and semiprimitive ringsrings with involutioncommutativity theorems. |
| spellingShingle | Joe W. Fisher Mohamed H. Fahmy On center-like elements in rings International Journal of Mathematics and Mathematical Sciences prime and semiprime rings primitive and semiprimitive rings rings with involution commutativity theorems. |
| title | On center-like elements in rings |
| title_full | On center-like elements in rings |
| title_fullStr | On center-like elements in rings |
| title_full_unstemmed | On center-like elements in rings |
| title_short | On center-like elements in rings |
| title_sort | on center like elements in rings |
| topic | prime and semiprime rings primitive and semiprimitive rings rings with involution commutativity theorems. |
| url | http://dx.doi.org/10.1155/S0161171285000138 |
| work_keys_str_mv | AT joewfisher oncenterlikeelementsinrings AT mohamedhfahmy oncenterlikeelementsinrings |