Relatively free *-bands (Q1580088)

A *-band is an idempotent semigroup equipped with a unary operation \(x\mapsto x^*\) satisfying \((x^*)^*=x\), \((xy)^*=y^*x^*\), \(x=xx^*x\). All varieties of *-bands have been found by \textit{C. Adair} [J. Algebra 75, 297-314 (1982; Zbl 0501.20040)]. The authors construct free objects in each of these varieties by solving the corresponding word problem on the free involutorial semigroup.