M. ASHRAF and M. A. QUADRI

Some commutativity theorems for torsion free rings

Pages: 241-245
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=[ x^m, yⁿ ]; (ii) [ xⁿ, yⁿ ]=0: (iii) x^t[xⁿ, y ]=[ x, y^m ]x^q; (iv) x^t[ xⁿ, y ]=[ x^m, y]y^m. 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.