RINGS WITH ASSOCIATORS IN THE COMMUTATIVE CENTER

Abstract

Thedy has introduced the subject of rings which satisfy the identity [(R, R, R), R] = 0 and which satisfy one additional identity such as (x, x, x) = 0. By assuming char.  2, 3 and simplicity, Thedy proved that R must be either commutative or associative. Kleinfeld proved that the additional identity assumed by Thedy is not necessary. Using Kleinfeld’s method, Suvarna et.al prove that if R is a simple ring of char.  3 satisfying [(R, R, R), R] = 0, then (x, x, x) = 0 for all x in R. From this R is either commutative or associative. This paper gives an alter proof of suvarna’s method.