  Let A be an algebra whose group of units U(A) satisfies a Laurent polynomial
identity (LPI). We establish conditions on these polynomials in such a way that
nil-generated algebras and group algebras with torsion groups over infinite
fields in characteristic p > 0 have nonmatrix identities. We also determine, in
the determine in the context of group algebras with arbitrary LPI for the group
of units, the existence of polynomial identities.
