Commutativity of one sided s-unital rings through a Streb's result. (1997) - Quadri, Murtaza A.; Jacob, V. W.; Ashraf, M.
Abstract : The main theorem proved in the present paper states as follows Letm, k, n ands be fixed non-negative integers such thatk andn are not simultaneously equal to1 andR be a left (resp right)s -unital ring satisfying[ ( x m y k ) n − x s y, x ] = 0 (resp[ ( x m y k ) n − y x s, x ] = 0 ) ThenR is commutative. Further commutativity of lefts -unital rings satisfying the conditionx t [ x m, y ] − y r [ x, f ( y ) ] x s = 0 wheref ( t ) ∈ t 2 Z [ t ] andm > 0, t, r ands 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 elementsx andy for their values. These results generalize a number of commutativity theorems established recently.