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Canonical Varieties of Completely Regular Semigroups

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

Mario Petrich
Mario Petrich
Affiliation:
21420 Bol, Brač Croatia
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Abstract

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Completely regular semigroups CR are regarded here as algebras with multiplication and the unary operation of inversion. Their lattice of varieties is denoted by L(CR). Let B denote the variety of bands and L(B) the lattice of its subvarieties. The mapping V → V ∩ B is a complete homomorphism of L(CR) onto L(B). The congruence induced by it has classes that are intervals, say VB = [VB, VB] for V ∈ L(CR). Here VB = V ∩ B. We characterize VB in several ways, the principal one being an inductive way of constructing bases for v-irreducible band varieties. We term the latter canonical. We perform a similar analysis for the intersection of these varieties with the varieties BG, OBG and B.

Keywords

completely regular semigroupvarietybandcongruenceintervalPolák's theoremladder.

MSC classification

Secondary: 20M07: Varieties and pseudovarieties of semigroups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 83 , Issue 1 , August 2007 , pp. 87 - 104
Copyright
Copyright © Australian Mathematical Society 2007

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