Some Polynomial Identities that Imply Commutativity of Rings
نویسنده
چکیده
In this paper, we establish some commutativity theorems for certain rings with polynomial constraints as follows: Let R be an associative ring, and for all x, y ∈ R, and fixed non-negative integers m > 1, n ≥ 0, r > 0, s ≥ 0, t ≥ 0, p ≥ 0, q ≥ 0 such that P (x, y) = ±Q(x, y), where P (x, y) = ys[x, y]yt and Q(x, y) = xp[xm, yn]ryq. First,it is shown that a semiprime ring R is commutative if and only if R satisfies the above conditions together with some constraints. Secondly, we investigate the commutativity of rings with identity if it satisfies some related polynomial identities, and then these results are extended to one sided s-unital rings.Finally, we give some examples and open problems that appreciate our results.
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