ON PSEUDO-COMMUTATMTY AND COMMUTATIVITY IN RINGS

Abstract

A ring R is called pseudo-commutative if for each x,y ε R there exists an integer n = n(x, y) for which xy = nyx. We first show that a generalization of a commutativity condition of Chacron and Thierrin implies pseudo-commutativity in rings; we then study pseudo-commutativity and commutativity in rings with constraints of the form xy = σk_iyⁱxⁱ, where the k_i are integers.