Word problems for free objects in certain varieties of completely regular semigroups

James Arthur Gerhard and Mario Petrich

Vol. 104 (1983), No. 2, 351–359

DOI: 10.2140/pjm.1983.104.351

Abstract

Semigroups which are unions of groups are said to be completely regular. They form a variety when considered as semigroups with an operation of inverse. The variety of bands and the variety of completely simple semigroups are subvarieties. The present paper reduces the word problem for the free semigroups in each subvariety 𝒱 of the join of the variety of bands and the variety of completely simple semigroups to the word problem for certain groups in 𝒱. In particular if the word problems for the latter have a solution so does the word problem in 𝒱.

Mathematical Subject Classification 2000

Primary: 20M05

Milestones

Received: 13 October 1980

Revised: 16 February 1982

Published: 1 February 1983