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## Discussiones Mathematicae - General Algebra and Applications

2001 | 21 | 2 | 255-268
Tytuł artykułu

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

Autorzy
Treść / Zawartość
Warianty tytułu
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
Kategorie tematyczne
Rocznik
Tom
Numer
Strony
255-268
Opis fizyczny
Daty
wydano
2001
otrzymano
2001-09-24
Twórcy
autor
• Mathematical Institute of the Polish Academy of Sciences, Kopernika 18, 51-617 Wrocław, Poland
Bibliografia
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• [14] J. Płonka, On n-clone extensions of algebras, Algebra Universalis 40 (1998), 1-17.
• [15] J. Płonka, Free algebras over biregularization of varieties, Acta Appl. Math. 52 (1998), 305-313.
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• [19] J. Płonka. and Z. Szylicka, Subdirectly irreducible generalized sums of upper semilattice ordered systems of algebras, Algebra Universalis (in print).
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