Semigroups generated by certain operators on varieties of completely regular semigroups

Mario Petrich and Norman R. Reilly

Vol. 132 (1988), No. 1, 151–175

DOI: 10.2140/pjm.1988.132.151

Abstract

The operators C, K, L, T, T_l and T_r on the lattice ℒ(𝒞ℛ) of varieties of completely regular semigroups have played an important role in recent studies of ℒ(𝒞ℛ). Although each of these operators is idempotent, when applied in various combinations to the trivial variety they yield varieties for which the only upper bound is 𝒞ℛ. The semigroups generated by various subsets of {C,K,L,T,T_r,T_l} are determined here in terms of generators and relations.

Mathematical Subject Classification 2000

Primary: 20M07

Milestones

Received: 10 July 1986

Revised: 12 December 1986

Published: 1 March 1988