COMMUTATIVITY THEOREMS FOR RINGS WITH CONSTRAINTS ON COMMUTATORS

Authors

  • H. A. S. ABUJABAL Department of Mathematics, Faculty of Science, King Abdul Aziz University, P.O. Box 31464, Jeddah 21497, Saudi Arabia.
  • MOHD ASHRAF Department of Mathematics, Aligarh Muslim University, Aligarh - 202 002 - India.

DOI:

https://doi.org/10.5556/j.tkjm.26.1995.4375

Keywords:

s-unital rings, factor subrings, polynomial identity, semiprime rings, commutators

Abstract

Let $R$ be a left (resp. right) $s$-unital ring and $m$ be a positive integer. Suppose that for each $y$ in $R$ there exist $J(t)$, $g(t)$, $h(t)$ in $Z[t]$ such that $x^m[x,y]= g(y)[x,y^2f(y)]h(y)$ (resp. $[x,y]x^m= g(y)[x,y^2f(y)]h(y))$ for all $x$ in $R$. Then $R$ is commutative (and conversely). Finally, the result is extended to the case when the exponent $m$ depends on the choice of $x$ and $y$.

References

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Published

1995-03-01

How to Cite

ABUJABAL, H. A. S., & ASHRAF, M. (1995). COMMUTATIVITY THEOREMS FOR RINGS WITH CONSTRAINTS ON COMMUTATORS. Tamkang Journal of Mathematics, 26(1), 25–29. https://doi.org/10.5556/j.tkjm.26.1995.4375

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