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Subdirect decompositions of the lattice of varieties of completely regular semigroups

Published online by Cambridge University Press:  17 April 2009

P.G. Trotter
P.G. Trotter
Affiliation:
Department of Mathematics, University of Tasmania, Hobart, Tasmania 7000, Australia
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Abstract

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It is shown that if V is an element of the lattice of the title then the map given by U → (V ∧ U, V ∨ U) is a complete lattice embedding of into (V] × [V) if and only if V is a join-infinitely distributive element. In this case the image of the map is a subdirect product of the principal ideal (V] by the principal filter [V) generated by V. Some important varieties in are shown to be join-infinitely distributive.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 39 , Issue 3 , June 1989 , pp. 343 - 351
Copyright
Copyright © Australian Mathematical Society 1989

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