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A special sublattice of the congruence lattice of a regular semigroup

Published online by Cambridge University Press:  20 January 2009

Mario Petrich
Mario Petrich
Affiliation:
Departamento De Matemática Pura, Faculdade De Ciências, Universidade Do Porto, P. Gomes Teixeira, 4050 Porto, Portugal
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Abstract

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Let S be a regular semigroup and be its congruence lattice. For ρ ∈ , we consider the sublattice Lρ of generated by the congruences pw where w ∈ {K, k, T, t}* and w has no subword of the form KT, TK, kt, tk. Here K, k, T, t are the operators on induced by the kernel and the trace relations on . We find explicitly the least lattice L whose homomorphic image is Lρ for all ρ ∈ and represent it as a distributive lattice in terms of generators and relations. We also consider special cases: bands of groups, E-unitary regular semigroups, completely simple semigroups, rectangular groups as well as varieties of completely regular semigroups.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 40 , Issue 3 , October 1997 , pp. 457 - 472
Copyright
Copyright © Edinburgh Mathematical Society 1997

References

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