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Congruences on an orthodox semigroup via the minimum inverse semigroup congruence

Published online by Cambridge University Press:  18 May 2009

Carl Eberhart  and
Wiley Williams
Carl Eberhart
Affiliation:
Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506, U.S.A.
Wiley Williams
Affiliation:
Department of Mathematics, University of Louisville, Louisville, Kentucky 40208, U.S.A.
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It is well known that the lattice Λ(S) of congruences on a regular semigroup S contains certain fundamental congruences. For example there is always a minimum band congruence β, which Spitznagel has used in his study of the lattice of congruences on a band of groups [16]. Of key importance to his investigation is the fact that β separates congruences on a band of groups in the sense that two congruences are the same if they have the same meet and join with β. This result enabled him to characterize θ-modular bands of groups as precisely those bands of groups for which ρ⃗(ρ∨β, ρ∧β)is an embedding of Λ(S) into a product of sublattices.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 18 , Issue 2 , July 1977 , pp. 181 - 192
Copyright
Copyright © Glasgow Mathematical Journal Trust 1977

References

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