Abstract
x , y , z s x , z , y 1 Ž . Ž . Ž . Ž . w x Ž . have been studied. Among these are rings of type 1, 1 2 , which satisfy 1 Ž . Ž . w x and x, x, x s 0, third power associativity , Novikov rings 4, 6, 7, 10 , Ž . Ž . Ž . which satisfy 1 and x yz s y xz , and more recently rings which satisfy Ž . Ž w x . w x 1 and w, y, z , s s 0, 1, 8 . In the present paper we study rings Ž . Ž Ž . . Ž . satisfying 1 and w, x, x, x , y s 0. This generalizes rings of type 1, 1 . Ž w x . w 2 x Ž . It also generalizes the identity w, y, z , s s 0, since x , x s x, x, x . The result we obtain is that simple rings of characteristic / 2, 3, 5 must be associative. There exist examples of simple Novikov rings which are not w x associative 3 , and there exist examples of right alternative division rings Ž Ž .. w x of characteristic 2 thus of type 1, 1 which are not associative 9 .
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