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On the lattice of congruences on a semilattice

Published online by Cambridge University Press:  09 April 2009

T. E. Hall
T. E. Hall
Affiliation:
Monash UniversityClayton
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Lattices of congruences are studied in section II.6 of Cohn [2]. Papers [5] and [6] by Munn deal with lattices of congruences on semigroups and conditions under which these lattices are modular. In [4] Lallement shows that the lattice of congruences on a completely 0-simple semigroup is semimodular, giving an alternative proof of the result, due to Preston [7], that the lattice of congruences on a completely 0-simple semigroup satisfies a certain chain condition which is a natural extension to arbitrary lattices of the Jordan-Dedekind chain condition for finite lattices.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 12 , Issue 4 , November 1971 , pp. 456 - 460
Copyright
Copyright © Australian Mathematical Society 1971

References

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