In:
Journal of the Australian Mathematical Society, Cambridge University Press (CUP), Vol. 83, No. 1 ( 2007-08), p. 87-104
Abstract:
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 V B = [ V B , V B ] for V ∈ L ( CR ). Here V B = V ∩ B . We characterize V B 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 .
Type of Medium:
Online Resource
ISSN:
1446-7887
,
1446-8107
DOI:
10.1017/S1446788700036405
Language:
English
Publisher:
Cambridge University Press (CUP)
Publication Date:
2007
detail.hit.zdb_id:
1478743-X
SSG:
17,1
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