  Let K be a field of positive characteristic p, let R be either a group
algebra K[G] or a restricted enveloping algebra u(L), and let I be the
augmentation ideal of R. We first characterize those R for which I satisfies a
polynomial identity not satisfied by the algebra of all 2-by-2 matrices over K.
Then we examine those R for which I satisfies a semigroup identity (that is, a
polynomial identity which can be written as the difference of two monomials).
