Abstract
Let Wr( U , V ) denote the variety of inverse semigroups generated by wreath products of semigroups in U with semigroups in V , where U and V are varieties of inverse semigroups. In this note we provide a description of the fully invariant congruence on the free inverse semigroup corresponding to Wr( U , V ) in terms of the fully invariant congruences corresponding to U and V . Some properties of varieties of this form are then presented.
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