Vol. 65, No. 2, 1976

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Standard regular semigroups

Ronson Joseph Warne

Vol. 65 (1976), No. 2, 539–562

We give a structure theorem for a class of regular semigroups. Let S be a regular semigroup, let T denote the union of the maximal subgroups of S, and let E(T) denote the set of idempotents of T. Assume T is a semigroup (equivalently, T is a semilattice Y of completely simple semigroups (Ty : y Y )). If Y has a greatest element and e,f,g E(T), e f, and e g imply fg = gf, we term S a standard regular semigroup. The structure of S is given modulo right groups and an inverse semigroup V in which every subgroup is a single element by means of an explict multiplication. We specialize the structure theorem to orthodox, -unipotent, and inverse semigroups, and to a class of semigroups with Y an ωY -semilattice.

Mathematical Subject Classification 2000
Primary: 20M10
Received: 23 May 1975
Revised: 12 April 1976
Published: 1 August 1976
Ronson Joseph Warne