International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 10, Pages 667-672
doi:10.1155/S0161171200004853

On structure of certain periodic rings and near-rings

Abstract

The aim of this work is to study a decomposition theorem for rings satisfying either of the properties xy=xpf(xyx)xq or xy=xpf(yxy)xq, where p=p(x,y),q=q(x,y) are nonnegative integers and f(t)∈tℤ[t] vary with the pair of elements x,y, and further investigate the commutativity of such rings. Other related results are obtained for near-rings.