Standard and Accessible Rings

Abstract

1. Introduction. A ring is defined to be standard (1) in case the following two identities hold :(1) (wx, y, z) + (xz, y, w) + (wz, y, x) = 0,(2) (x, y, z) + (z, x, y) − (x, z, y) = 0,where the associator (x, y, z) is defined by (x, y, z) = (xy)z − x(yz). Albert has determined the structure of finite-dimensional, standard algebras (1).The simple ones turn out to be either Jordan algebras or associative ones.