From twists to involution bands
Igor Dolinka · 2001
In this note 1 we give a representation theorem for involution bands. In addition, it is shown that the construction used in such a representation yields an operator on the lattice of involution band varieties. x1. By an involution semigroup we mean a semigroup S endowed with a unary operation ⁄ (called the involution) such that the identities (xy) ⁄ = y ⁄ x ⁄ and (x ⁄ ) ⁄ = x are satisfied. Groups and, more generally, inverse semigroups are clearly the most natural examples of involution semigroups. The intensive study of involution semigroups began with the paper of Nordahl and Scheiblich [15], where involution semigroups with the additional identity xx ⁄ x = x, called regular ⁄ -semigroups (or just ⁄ -semigroups for short), were considered.