• RINGS WITH (a, b, a) AND COMMUTATORS IN THE RIGHT NUCLEUS

Abstract

In this paper we show that if R is a nonassociative simple ring satisfying (a, b, a) and (R, R) are in the right nucleus N_r, then (a, b, a) and (R, R) are in the left and middle nuclei of R. Using these properties we prove that (a, b, a) and (R, R) are in the center C of R. Also it is shown that R is commutative.