Minimal generics from subvarieties of the clone extension of the variety of Boolean algebras

Jerzy Płonka

Colloquium Mathematicae (2008)

  • Volume: 112, Issue: 1, page 131-145
  • ISSN: 0010-1354

Abstract

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Let τ be a type of algebras without nullary fundamental operation symbols. We call an identity φ ≈ ψ of type τ clone compatible if φ and ψ are the same variable or the sets of fundamental operation symbols in φ and ψ are nonempty and identical. For a variety of type τ we denote by c the variety of type τ defined by all clone compatible identities from Id(). We call c the clone extension of . In this paper we describe algebras and minimal generics of all subvarieties of c , where is the variety of Boolean algebras.

How to cite

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Jerzy Płonka. "Minimal generics from subvarieties of the clone extension of the variety of Boolean algebras." Colloquium Mathematicae 112.1 (2008): 131-145. <http://eudml.org/doc/284330>.

@article{JerzyPłonka2008,
abstract = {Let τ be a type of algebras without nullary fundamental operation symbols. We call an identity φ ≈ ψ of type τ clone compatible if φ and ψ are the same variable or the sets of fundamental operation symbols in φ and ψ are nonempty and identical. For a variety of type τ we denote by $^\{c\}$ the variety of type τ defined by all clone compatible identities from Id(). We call $^\{c\}$ the clone extension of . In this paper we describe algebras and minimal generics of all subvarieties of $^\{c\}$, where is the variety of Boolean algebras.},
author = {Jerzy Płonka},
journal = {Colloquium Mathematicae},
keywords = {Boolean algebra; clone compatible identity; clone extension of a variety; minimal generic},
language = {eng},
number = {1},
pages = {131-145},
title = {Minimal generics from subvarieties of the clone extension of the variety of Boolean algebras},
url = {http://eudml.org/doc/284330},
volume = {112},
year = {2008},
}

TY - JOUR
AU - Jerzy Płonka
TI - Minimal generics from subvarieties of the clone extension of the variety of Boolean algebras
JO - Colloquium Mathematicae
PY - 2008
VL - 112
IS - 1
SP - 131
EP - 145
AB - Let τ be a type of algebras without nullary fundamental operation symbols. We call an identity φ ≈ ψ of type τ clone compatible if φ and ψ are the same variable or the sets of fundamental operation symbols in φ and ψ are nonempty and identical. For a variety of type τ we denote by $^{c}$ the variety of type τ defined by all clone compatible identities from Id(). We call $^{c}$ the clone extension of . In this paper we describe algebras and minimal generics of all subvarieties of $^{c}$, where is the variety of Boolean algebras.
LA - eng
KW - Boolean algebra; clone compatible identity; clone extension of a variety; minimal generic
UR - http://eudml.org/doc/284330
ER -

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