Vol. 104, No. 2, 1983

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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
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
Authors
James Arthur Gerhard
Mario Petrich