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Discussiones Mathematicae General Algebra and Applications 21(2) (2001) 255-268
DOI: https://doi.org/10.7151/dmgaa.1042

THE LATTICE OF SUBVARIETIES OF THE BIREGULARIZATION OF THE VARIETY OF BOOLEAN ALGEBRAS

Jerzy Płonka

Mathematical Institute of the Polish Academy of Sciences
Kopernika 18, 51-617 Wrocław, Poland
e-mail: jersabi@wp.pl

Abstract

Let t:  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 j » y 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 t we denote by V_b the biregularization of V, i.e. the variety of type t defined by all biregular identities from Id (V).

Let B be the variety of Boolean algebras of type t_b:{+,·,˘}® N, where t_b(+) = t_b(·) = 2 and t_b(˘) = 1. In this paper we characterize the lattice L(B_b) of all subvarieties of the biregularization of the variety B.

Keywords: subdirectly irreducible algebra, lattice of subvarieties, Boolean algebra, biregular identity.

2000 Mathematics Subject Classification: 08B15.

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Received 24 September 2001