Rings with (x,y,z) = (x,z,y)

The earliest work on algebras satisfying the identity in the title belongs to A. A. Albert in the context of rings of (γ, δ) type, in particular rings of type. Novikov rings satisfy (x,y,z) = (x,z,y) and additionally x · yz = y · xz, but not (x, x, x) = 0. This additional identity can be weakened to (x, y, yz) = y(x, y, z) without much loss. This chapter revisits rings satisfying (x, y, z) = (x, z, y) and (x, x, x) = 0, and presents a much streamlined argument which shows that simple and the existence of a left identity implies associative.