A network of congruences on an inverse semigroup

Authors:
Mario Petrich and Norman R. Reilly

Journal:
Trans. Amer. Math. Soc. **270** (1982), 309-325

MSC:
Primary 20M10

DOI:
https://doi.org/10.1090/S0002-9947-1982-0642343-6

MathSciNet review:
642343

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Abstract | References | Similar Articles | Additional Information

Abstract: A congruence on an inverse semigroup is determined uniquely by its kernel and its trace. Denoting by and the least congruence on having the same kernel and the same trace as , respectively, and denoting by the universal congruence on , we consider the sequence , , , , . These congruences, together with the intersections of corresponding pairs, form a sublattice of the lattice of all congruences on . We study the properties of these congruences and establish several properties of the quasivarieties of inverse semigroups induced by them.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1982-0642343-6

Keywords:
Inverse semigroups,
congruences,
lattice of congruences,
implications,
kernel and trace of a congruence

Article copyright:
© Copyright 1982
American Mathematical Society