J Austral Math Soc Ser A 49 pp1--23, 1990.

Operators Related to Idempotent Generated and Monoid Completely Regular Semigroups

Mario Petrich and Norman R. Reilly

Abstract

The class CR of completely regular semigroups (unions of groups or algebras woth the associative binary operation of multiplication and the unary operation of inversion subject to the laws x = xx^-1x, (x^-1)^-1 and xx^-1 = x^-1x) is a variety. Among the important subclasses of CR are the classes M of monoids and I of idempotent generated members. For each C Î {I, M}, there are the associated mappings V ® V ÇC and V ® áV ÇCñ, the variety generated by V ÇC. The lattice theoretic properties of these mappings and the interactions between these mappings are studied.

1980 AMS Subject Classification (1985 Revision): 20M07, 20M10

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Authors

Mario Petrich

Norman R. Reilly

Simon Fraser University, Burnaby, B.C., Canada.