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

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Płonka J.

Discussiones Mathematicae - General Algebra and Applications

2001

tom 21

nr 2

255-268

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.

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1 Discussiones Mathematicae - General Algebra and Applications

1 Płonka J.

1 2001

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