Commutativity of one sided s-unital rings through a Streb's result
The main theorem proved in the present paper states as follows Let m, k, n and s be fixed non-negative integers such that k and n are not simultaneously equal to 1 and R be a left (resp right) s-unital ring satisfying [(xmyk)n−xsy,x]=0 (resp [(xmyk)n−yxs,x]=0) Then R is commutative. Further commutat...
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| Format: | Article |
| Language: | English |
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Wiley
1997-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171297000367 |
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| author | Murtaza A. Quadri V. W. Jacob M. Ashraf |
| author_facet | Murtaza A. Quadri V. W. Jacob M. Ashraf |
| author_sort | Murtaza A. Quadri |
| collection | DOAJ |
| description | The main theorem proved in the present paper states as follows Let m, k, n and s be
fixed non-negative integers such that k and n are not simultaneously equal to 1 and R be a left
(resp right) s-unital ring satisfying [(xmyk)n−xsy,x]=0 (resp [(xmyk)n−yxs,x]=0) Then R is
commutative. Further commutativity of left s-unital rings satisfying the condition xt[xm,y]−yr[x,f(y)]xs=0 where f(t)∈t2Z[t] and m>0,t,r and s are fixed non-negative integers, has been
investigated Finally, we extend these results to the case when integral exponents in the underlying
conditions are no longer fixed, rather they depend on the pair of ring elements x and y for their values.
These results generalize a number of commutativity theorems established recently. |
| format | Article |
| id | doaj-art-12b375b28bb44e6e81fe1872a055de0e |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1997-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-12b375b28bb44e6e81fe1872a055de0e2025-02-03T05:54:11ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251997-01-0120226727010.1155/S0161171297000367Commutativity of one sided s-unital rings through a Streb's resultMurtaza A. Quadri0V. W. Jacob1M. Ashraf2Department of Mathematics, Aligarh Muslim University, Aligarh 202002, IndiaDepartment of Mathematics, Aligarh Muslim University, Aligarh 202002, IndiaDepartment of Mathematics, Aligarh Muslim University, Aligarh 202002, IndiaThe main theorem proved in the present paper states as follows Let m, k, n and s be fixed non-negative integers such that k and n are not simultaneously equal to 1 and R be a left (resp right) s-unital ring satisfying [(xmyk)n−xsy,x]=0 (resp [(xmyk)n−yxs,x]=0) Then R is commutative. Further commutativity of left s-unital rings satisfying the condition xt[xm,y]−yr[x,f(y)]xs=0 where f(t)∈t2Z[t] and m>0,t,r and s are fixed non-negative integers, has been investigated Finally, we extend these results to the case when integral exponents in the underlying conditions are no longer fixed, rather they depend on the pair of ring elements x and y for their values. These results generalize a number of commutativity theorems established recently.http://dx.doi.org/10.1155/S0161171297000367factor subringss-unital ringspolynomial identitiescommutators. |
| spellingShingle | Murtaza A. Quadri V. W. Jacob M. Ashraf Commutativity of one sided s-unital rings through a Streb's result International Journal of Mathematics and Mathematical Sciences factor subrings s-unital rings polynomial identities commutators. |
| title | Commutativity of one sided s-unital rings through a Streb's result |
| title_full | Commutativity of one sided s-unital rings through a Streb's result |
| title_fullStr | Commutativity of one sided s-unital rings through a Streb's result |
| title_full_unstemmed | Commutativity of one sided s-unital rings through a Streb's result |
| title_short | Commutativity of one sided s-unital rings through a Streb's result |
| title_sort | commutativity of one sided s unital rings through a streb s result |
| topic | factor subrings s-unital rings polynomial identities commutators. |
| url | http://dx.doi.org/10.1155/S0161171297000367 |
| work_keys_str_mv | AT murtazaaquadri commutativityofonesidedsunitalringsthroughastrebsresult AT vwjacob commutativityofonesidedsunitalringsthroughastrebsresult AT mashraf commutativityofonesidedsunitalringsthroughastrebsresult |