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Certain congruence and quotient lattices related to completely 0-simple and primitive regular semigroups

Published online by Cambridge University Press:  18 May 2009

H. E. Scheiblich
H. E. Scheiblich
Affiliation:
University of South Carolina, Columbia, South Carolina
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G. Lallement [4] has shown that the lattice of congruences, Λ(S), on a completely 0-simple semigroup S is semimodular, thus improving G. B. Preston's result [5] that such a lattice satisfies the Jordan-Dedekind chain condition. More recently, J. M. Howie [2] has given a new and more simple proof of Lallement's result using work due to Tamura [9]. The purpose of this note is to extend the semimodularity result to primitive regular semigroups, to establish a theorem relating certain congruence and quotient lattices, and to provide a theorem for congruences on any regular semigroup.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 10 , Issue 1 , January 1969 , pp. 21 - 24
Copyright
Copyright © Glasgow Mathematical Journal Trust 1969

References

REFERENCES

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