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On a sublattice of the lattice of congruences on a simple regular ω-semigroup

Published online by Cambridge University Press:  09 April 2009

G. R. Baird
G. R. Baird
Affiliation:
Department of Mathematics, Monash University
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The set E of idemponents of a semigroup S can be partially ordered by defining e ≦f and only if ef = fe = e (e,f ∈ E). If E = {ei: i = i = 0,1…} and under this ordering e0 > e1 > e2… then we call S an ω-semigroup. Munn [10] has given a complete classification of simple regular ω-semigroups in terms of groups and group homomorphisms. Let ∧0(S) denote the set of congruences on a simple regular w-semigroup S consisting of those congruences which either are idempotent-separating or are group congruences on S. It is evident that ∧0(S) is a sublattice of the lattice of all congruences on S.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 13 , Issue 4 , June 1972 , pp. 461 - 471
Copyright
Copyright © Australian Mathematical Society 1972

References

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