The lattice of subvarieties of the biregularization of the variety of Boolean algebras

Jerzy Płonka

Discussiones Mathematicae - General Algebra and Applications (2001)

  • Volume: 21, Issue: 2, page 255-268
  • ISSN: 1509-9415

Abstract

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Let τ: F → N be a type of algebras, where F is a set of fundamental operation symbols and N is the set of all positive integers. An identity φ ≈ ψ is called biregular if it has the same variables in each of it sides and it has the same fundamental operation symbols in each of it sides. For a variety V of type τ we denote by V b the biregularization of V, i.e. the variety of type τ defined by all biregular identities from Id(V). Let B be the variety of Boolean algebras of type τ b : + , · , ´ → N , where τ b ( + ) = τ b ( · ) = 2 and τ b ( ´ ) = 1 . In this paper we characterize the lattice ℒ ( B b ) of all subvarieties of the biregularization of the variety B.

How to cite

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Jerzy Płonka. "The lattice of subvarieties of the biregularization of the variety of Boolean algebras." Discussiones Mathematicae - General Algebra and Applications 21.2 (2001): 255-268. <http://eudml.org/doc/287674>.

@article{JerzyPłonka2001,
abstract = {Let τ: F → N be a type of algebras, where F is a set of fundamental operation symbols and N is the set of all positive integers. An identity φ ≈ ψ is called biregular if it has the same variables in each of it sides and it has the same fundamental operation symbols in each of it sides. For a variety V of type τ we denote by $V_\{b\}$ the biregularization of V, i.e. the variety of type τ defined by all biregular identities from Id(V). Let B be the variety of Boolean algebras of type $τ_\{b\}: \{+,·,´\} → N$, where $τ_\{b\}(+) = τ_\{b\}(·) = 2$ and $τ_\{b\}(´) = 1$. In this paper we characterize the lattice $ℒ(B_\{b\})$ of all subvarieties of the biregularization of the variety B.},
author = {Jerzy Płonka},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {subdirectly irreducible algebra; lattice of subvarieties; Boolean algebra; biregular identity; variety of Boolean algebras; biregularization; biregular identities},
language = {eng},
number = {2},
pages = {255-268},
title = {The lattice of subvarieties of the biregularization of the variety of Boolean algebras},
url = {http://eudml.org/doc/287674},
volume = {21},
year = {2001},
}

TY - JOUR
AU - Jerzy Płonka
TI - The lattice of subvarieties of the biregularization of the variety of Boolean algebras
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2001
VL - 21
IS - 2
SP - 255
EP - 268
AB - Let τ: F → N be a type of algebras, where F is a set of fundamental operation symbols and N is the set of all positive integers. An identity φ ≈ ψ is called biregular if it has the same variables in each of it sides and it has the same fundamental operation symbols in each of it sides. For a variety V of type τ we denote by $V_{b}$ the biregularization of V, i.e. the variety of type τ defined by all biregular identities from Id(V). Let B be the variety of Boolean algebras of type $τ_{b}: {+,·,´} → N$, where $τ_{b}(+) = τ_{b}(·) = 2$ and $τ_{b}(´) = 1$. In this paper we characterize the lattice $ℒ(B_{b})$ of all subvarieties of the biregularization of the variety B.
LA - eng
KW - subdirectly irreducible algebra; lattice of subvarieties; Boolean algebra; biregular identity; variety of Boolean algebras; biregularization; biregular identities
UR - http://eudml.org/doc/287674
ER -

References

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