A Commutativity Study for Certain Rings

Abstract

Abstract. In this paper, we discuss with the polynomial identities of the formare fixed integers, and also they are different in the noncommutative situation. Firstly, it is shown that a semiprime ring is commutative if and only if it satisfies the above conditions. Secondly, commutativity of associative rings with unity 1 and without unit 1 have also been obtained if they satisfy above and related polynomial identities. Thirdly, the result for rings with unity 1 is extended to one-sided s-unital rings. Also, we give some examples that appreciate our results. Finally, we propose a problem for future endeavor.

Some commutativity results for certain rings

“…Finally, in Section 4, we establish commutativity of s-unital rings satisfying the property (see [5]) under appropriate torsion restrictions on commutators. Also several commutativity results can be obtained as corollaries to our results (see [4,5,8,10,12]).…”