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Discussiones Mathematicae General Algebra and Applications 20(1) (2000) 21-36
DOI: https://doi.org/10.7151/dmgaa.1002

THE GALOIS CORRESPONDENCE BETWEEN SUBVARIETY LATTICES AND MONOIDS OF HYPERSUBSTITUTIONS

Abstract

Denecke and Reichel have described a method of studying the lattice of all varieties of a given type by using monoids of hypersubstitutions. In this paper we develop a Galois correspondence between monoids of hypersubstitutions of a given type and lattices of subvarieties of a given variety of that type. We then apply the results obtained to the lattice of varieties of bands (idempotent semigroups), and study the complete sublattices of this lattice obtained through the Galois correspondence.

Keywords: hypersubstitutions, hyperidentities, M-hyperidentities, monoids of hypersubstitutions, varieties, solid varieties, M-solid varieties of bands, Galois correspondence.

1991 Mathematics Subject Classification: 08A40, 08B15, 08B05, 20M07, 06A15.

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Received 30 October 1997
Revised 11 June 1999