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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1997-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171297000367 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |