Completely semisimple inverse Δ-semigroups admitting principal series

Peter George Trotter and Takayuki Tamura

Vol. 68 (1977), No. 2, 515–525

DOI: 10.2140/pjm.1977.68.515

Abstract

A Δ-semigroup is a semigroup whose lattice of congruences is a chain with respect to inclusion. A completely semisimple inverse Δ-semigroup that admits a principal series is characterized here as a semigroup that results from a particular series of ideal extensions of Brandt semigroups by Brandt semigroups. A characterization is given of finite inverse Δ-semigroups in terms of groups, Brandt semigroups, and one to one partial transformations of sets.

Mathematical Subject Classification 2000

Primary: 20M10

Milestones

Received: 7 November 1975

Revised: 13 September 1976

Published: 1 February 1977