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Certain fundamental congruences on a regular semigroup†

Published online by Cambridge University Press:  18 May 2009

J. M. Howie  and
G. Lallement
J. M. Howie
Affiliation:
University of GlasgowGlasgow, W. 2
G. Lallement
Affiliation:
Institut Henri PoincaréParis
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In recent developments in the algebraic theory of semigroups attention has been focussing increasingly on the study of congruences, in particular on lattice-theoretic properties of the lattice of congruences. In most cases it has been found advantageous to impose some restriction on the type of semigroup considered, such as regularity, commutativity, or the property of being an inverse semigroup, and one of the principal tools has been the consideration of special congruences. For example, the minimum group congruence on an inverse semigroup has been studied by Vagner [21] and Munn [13], the maximum idempotent-separating congruence on a regular or inverse semigroup by the authors separately [9, 10] and by Munn [14], and the minimum semilattice congruence on a general or commutative semigroup by Tamura and Kimura [19], Yamada [22], Clifford [3] and Petrich [15]. In this paper we study regular semigroups and our primary concern is with the minimum group congruence, the minimum band congruence and the minimum semilattice congruence, which we shall consistently denote by α β and η respectively.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 7 , Issue 3 , January 1966 , pp. 145 - 159
Copyright
Copyright © Glasgow Mathematical Journal Trust 1966

References

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