The Galois correspondence between subvariety lattices and monoids of hpersubstitutions

Klaus Denecke; Jennifer Hyndman; Shelly L. Wismath

Discussiones Mathematicae - General Algebra and Applications (2000)

  • Volume: 20, Issue: 1, page 21-36
  • ISSN: 1509-9415

Abstract

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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.

How to cite

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Klaus Denecke, Jennifer Hyndman, and Shelly L. Wismath. "The Galois correspondence between subvariety lattices and monoids of hpersubstitutions." Discussiones Mathematicae - General Algebra and Applications 20.1 (2000): 21-36. <http://eudml.org/doc/287704>.

@article{KlausDenecke2000,
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.},
author = {Klaus Denecke, Jennifer Hyndman, Shelly L. Wismath},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {hypersubstitutions; hyperidentities; M-hyperidentities; monoids of hypersubstitutions; varieties; solid varieties; M-solid varieties of bands; Galois correspondence; monoid; lattice of varieties of bands; complete sublattices},
language = {eng},
number = {1},
pages = {21-36},
title = {The Galois correspondence between subvariety lattices and monoids of hpersubstitutions},
url = {http://eudml.org/doc/287704},
volume = {20},
year = {2000},
}

TY - JOUR
AU - Klaus Denecke
AU - Jennifer Hyndman
AU - Shelly L. Wismath
TI - The Galois correspondence between subvariety lattices and monoids of hpersubstitutions
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2000
VL - 20
IS - 1
SP - 21
EP - 36
AB - 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.
LA - eng
KW - hypersubstitutions; hyperidentities; M-hyperidentities; monoids of hypersubstitutions; varieties; solid varieties; M-solid varieties of bands; Galois correspondence; monoid; lattice of varieties of bands; complete sublattices
UR - http://eudml.org/doc/287704
ER -

References

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