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Harmonic inverse semigroups

Published online by Cambridge University Press:  18 May 2009

Mario Petrich  and
Stuart A. Rankin
Mario Petrich
Affiliation:
University of Western Ontario, London, Canada
Stuart A. Rankin
Affiliation:
University of Western Ontario, London, Canada
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An inverse semigroup S shall be said to be harmonic if every congruence on S is determined by any one of its classes. In other words, if λ and ρ are congruences on S having a congruence class in common, then λ = ρ. The class of all harmonic semigroups contains all bisimple inverse semigroups, as proved by Žitomirskiĭ [11] and also by Schein [10], and all congruence-free inverse semigroups. Moreover, is contained in the class of all 0-simple or simple inverse semigroups, as is easy to see. We shall show that there exist non-bisimple, non-congruence-free harmonic semigroups and that there are simple inverse semigroups which are not harmonic.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 31 , Issue 3 , September 1989 , pp. 335 - 351
Copyright
Copyright © Glasgow Mathematical Journal Trust 1989

References

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