Commutativity of Associative Rings through Astreb
نویسنده
چکیده
Let m 0; r 0; s 0; q 0 be xed integers. Suppose that R is an associative ring with unity 1 in which for each x; y 2 R there exist polynomials f(X) 2 X 2 Z ZX]; g(X); h(X) 2 XZ ZX] such that f1?g(yx m)gx; x r y ? x s f(yx m)x q ]f1?h(yx m)g = 0. Then R is commu-tative. Further, result is extended to the case when the integral exponents in the above property depend on the choice of x and y. Finally, commutativity of one sided s-unital ring is also obtained when R satisses some related ring properties.
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