On commutativity of one-sided s-unital rings
The following theorem is proved: Let r=r(y)>1, s, and t be non-negative integers. If R is a left s-unital ring satisfies the polynomial identity [xy−xsyrxt,x]=0 for every x,y∈R, then R is commutative. The commutativity of a right s-unital ring satisfying the polynomial identity [xy−yrxt,x]=0 for...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
1992-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171292001078 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832556165197725696 |
|---|---|
| author | H. A. S. Abujabal M. A. Khan |
| author_facet | H. A. S. Abujabal M. A. Khan |
| author_sort | H. A. S. Abujabal |
| collection | DOAJ |
| description | The following theorem is proved: Let r=r(y)>1, s, and t be non-negative integers. If R is a left s-unital ring satisfies the polynomial identity [xy−xsyrxt,x]=0 for every x,y∈R, then R is commutative. The commutativity of a right s-unital ring satisfying the polynomial identity [xy−yrxt,x]=0 for all x,y∈R, is also proved. |
| format | Article |
| id | doaj-art-de70f3f1cee04245a9863b960c49db9d |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1992-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-de70f3f1cee04245a9863b960c49db9d2025-02-03T05:46:11ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251992-01-0115481381810.1155/S0161171292001078On commutativity of one-sided s-unital ringsH. A. S. Abujabal0M. A. Khan1Department of Mathematics, Faculty of Science, King Abdul Aziz University, P. O. Box 31464, Jeddah 21497, Saudi ArabiaDepartment of Mathematics, Faculty of Science, King Abdul Aziz University, P. O. Box 31464, Jeddah 21497, Saudi ArabiaThe following theorem is proved: Let r=r(y)>1, s, and t be non-negative integers. If R is a left s-unital ring satisfies the polynomial identity [xy−xsyrxt,x]=0 for every x,y∈R, then R is commutative. The commutativity of a right s-unital ring satisfying the polynomial identity [xy−yrxt,x]=0 for all x,y∈R, is also proved.http://dx.doi.org/10.1155/S0161171292001078commutativity of ringsleft s-unital ringsring with unitynilpotent elementsnil commutator idealzero-divisorssemi-prime rings. |
| spellingShingle | H. A. S. Abujabal M. A. Khan On commutativity of one-sided s-unital rings International Journal of Mathematics and Mathematical Sciences commutativity of rings left s-unital rings ring with unity nilpotent elements nil commutator ideal zero-divisors semi-prime rings. |
| title | On commutativity of one-sided s-unital rings |
| title_full | On commutativity of one-sided s-unital rings |
| title_fullStr | On commutativity of one-sided s-unital rings |
| title_full_unstemmed | On commutativity of one-sided s-unital rings |
| title_short | On commutativity of one-sided s-unital rings |
| title_sort | on commutativity of one sided s unital rings |
| topic | commutativity of rings left s-unital rings ring with unity nilpotent elements nil commutator ideal zero-divisors semi-prime rings. |
| url | http://dx.doi.org/10.1155/S0161171292001078 |
| work_keys_str_mv | AT hasabujabal oncommutativityofonesidedsunitalrings AT makhan oncommutativityofonesidedsunitalrings |