Commutativity of one sided s-unital rings through a Streb's result. (1997)

• Record Type: Journal Article
• Authors: Quadri, Murtaza A.; Jacob, V. W.; Ashraf, M.
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 20:Number 2(1997)
• Page Start: 267
• Page End: 270
• Publication Date: 1997
• Subjects: factor subrings -- s-unital rings -- polynomial identities -- commutators; Mathematics -- Periodicals; 510.5
• DOI: 10.1155/S0161171297000367
• Languages: English
• ISSNs: 0161-1712

Abstract

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.