# 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

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topEwa 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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