Abstract. Rings satisfying various identities of the form $x_1\cdots x_n=w(x_1,\ldots,x_n)$, $|w|>n\ge2$, have been considered many times. The purpose of this paper is to give a structural theorem for rings satisfying an arbitrary identity of this form. We introduce the notion of characteristic quadruplet $(n,p,h,t)$ of such an identity, and using it we characterize rings satisfying this identity as ideal extensions of an $n$-nilpotent ring by a ring satisfying $x=x^{p+1}$ and satisfying also some additional conditions, determined by the numbers $h$ and $t$, on nilpotents, idempotents and regular elements.

AMS Subject Classification (1991): 16A30

Received March 17, 1995. (Registered under 5675/2009.)