The dimension of a variety

Ewa Graczyńska; Dietmar Schweigert

Discussiones Mathematicae - General Algebra and Applications (2007)

  • Volume: 27, Issue: 1, page 35-47
  • ISSN: 1509-9415

Abstract

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Derived varieties were invented by P. Cohn in [4]. Derived varieties of a given type were invented by the authors in [10]. In the paper we deal with the derived variety V σ of a given variety, by a fixed hypersubstitution σ. We introduce the notion of the dimension of a variety as the cardinality κ of the set of all proper derived varieties of V included in V. We examine dimensions of some varieties in the lattice of all varieties of a given type τ. Dimensions of varieties of lattices and all subvarieties of regular bands are determined.

How to cite

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Ewa Graczyńska, and Dietmar Schweigert. "The dimension of a variety." Discussiones Mathematicae - General Algebra and Applications 27.1 (2007): 35-47. <http://eudml.org/doc/276936>.

@article{EwaGraczyńska2007,
abstract = {Derived varieties were invented by P. Cohn in [4]. Derived varieties of a given type were invented by the authors in [10]. In the paper we deal with the derived variety $V_\{σ\}$ of a given variety, by a fixed hypersubstitution σ. We introduce the notion of the dimension of a variety as the cardinality κ of the set of all proper derived varieties of V included in V. We examine dimensions of some varieties in the lattice of all varieties of a given type τ. Dimensions of varieties of lattices and all subvarieties of regular bands are determined.},
author = {Ewa Graczyńska, Dietmar Schweigert},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {derived algebras; derived varieties; the dimension of a variety; variety; hypersubstitution; derived algebra; derived variety; dimension; lattice; idempotent semigroup},
language = {eng},
number = {1},
pages = {35-47},
title = {The dimension of a variety},
url = {http://eudml.org/doc/276936},
volume = {27},
year = {2007},
}

TY - JOUR
AU - Ewa Graczyńska
AU - Dietmar Schweigert
TI - The dimension of a variety
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2007
VL - 27
IS - 1
SP - 35
EP - 47
AB - Derived varieties were invented by P. Cohn in [4]. Derived varieties of a given type were invented by the authors in [10]. In the paper we deal with the derived variety $V_{σ}$ of a given variety, by a fixed hypersubstitution σ. We introduce the notion of the dimension of a variety as the cardinality κ of the set of all proper derived varieties of V included in V. We examine dimensions of some varieties in the lattice of all varieties of a given type τ. Dimensions of varieties of lattices and all subvarieties of regular bands are determined.
LA - eng
KW - derived algebras; derived varieties; the dimension of a variety; variety; hypersubstitution; derived algebra; derived variety; dimension; lattice; idempotent semigroup
UR - http://eudml.org/doc/276936
ER -

References

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