The free algebra in the subvarieties of the variety of regular bands

AbstractA semigroup S is called a regular band if the laws xx = x and xyxzx = xyzx hold in S. For all subvarieties of the variety of regular bands a set-theoretic description of the free algebra is given. Moreover, it is proved that for fixed set of free generators these free algebras are subalgebras of the direct product of five elementary semigroups