M. ASHRAF and M. A. QUADRI
Some commutativity theorems for torsion free rings
Received: 28 June 1991
Mathematics Subject Classification: 16A70
Abstract: In the present paper we have investigated the commutativity of associative rings under the following conditions: (i) [ x,y ]k=[ xm, yn ]; (ii) [ xn, yn ]=0: (iii) xt[xn, y ]=[ x, ym ]xq; (iv) xt[ xn, y ]=[ xm, y]ym. We prove that every torsion-free ring satisfying any of (i)-(iv) is commutative. This allows us to extend several known results and to obtain a simple proof of a theorem of Awtar.