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

• Autorzy: Jerzy Płonka
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

subdirectly irreducible algebra; lattice of subvarieties; Boolean algebra; biregular identity

Kategorie tematyczne

• 08B15: Lattices of varieties

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2001
• Tom: 21
• Numer: 2
• Strony: 255-268

Daty

wydano

2001

otrzymano

2001-09-24

Twórcy

autor

Jerzy Płonka

• Mathematical Institute of the Polish Academy of Sciences, Kopernika 18, 51-617 Wrocław, Poland

Bibliografia

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Identyfikatory

DOI

10.7151/dmgaa.1042