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

Jerzy Płonka

Jerzy Płonka

Discussiones Mathematicae - General Algebra and Applications, Tome 21 (2001), p. 255-268 / Harvested from The Polish Digital Mathematics Library

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Résumé

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 $τ_{b} : +, \cdot, ´ \to N$ , where $τ_{b} (+) = τ_{b} (\cdot) = 2$ and $τ_{b} (´) = 1$ . In this paper we characterize the lattice $ℒ (B_{b})$ of all subvarieties of the biregularization of the variety B.

Publié le : 2001-01-01

Zbl 1005.08002

EUDML-ID : urn:eudml:doc:287674

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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, Tome 21 (2001) pp. 255-268. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1042/

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