Regular \(*\)-semigroup varieties with the amalgamation property.
A regular *-semigroup is a semigroup with involution \(x\to x^*\) such that \(x^*\) is always an inverse of \(x\). Examples include inverse semigroups with the usual inverse as involution. Orthodox and completely simple *-semigroups have also been studied extensively. All varieties of inverse semigroups with either the weak or strong amalgamation property were determined, modulo group varieties, by \textit{T. E. Hall} [Semigroup Forum 16, 37-51 (1978; Zbl 0396.20039)]. In this paper the author to a large extent determines the regular *-semigroup varieties that have the weak or strong amalgamation property: they are either inverse semigroup varieties with the corresponding property, the joins of such varieties with the variety of *-rectangular bands, or completely simple *-semigroups with the corresponding property. The author notes that for locally finite varieties, a complete determination then follows, along the lines of \textit{M. V. Sapir} [Colloq. Math. Soc. János Bolyai 39, 377-387 (1985; Zbl 0627.20034)].
scientific article; zbMATH DE number 2078230
scientific article