In  Schafer has defined generalized standard rings as rings satisfying the identities
and observed that these identities imply (y,y, (x, z)) = 0 and if the characteristic is not three, (x, y, x
2) = 0. Schafer determined the structure of simple, finite-dimensional generalized standard algebras of characteristic not two or three by showing that they must be either commutative, Jordan, or alternative.
Previously one of us  had studied accessible rings, which are defined by the identities (x,y,z) + (z,x,y) – (x,z,y) = 0 and ((w,x), y,z) = 0.