The lattice of subvarieties of the biregularization of the variety of Boolean algebras
Discussiones Mathematicae. General Algebra and Applications, Tome 21 (2001) no. 2, pp. 255-268.

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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).
Keywords: subdirectly irreducible algebra, lattice of subvarieties, Boolean algebra, biregular identity
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Płonka, Jerzy. The lattice of subvarieties of the biregularization of the variety of Boolean algebras. Discussiones Mathematicae. General Algebra and Applications, Tome 21 (2001) no. 2, pp. 255-268. http://geodesic.mathdoc.fr/item/DMGAA_2001_21_2_a9/

[1] S. Burris and H.P. Sankappanavar, A Course in Universal Algebra, Springer-Verlag, New York-Heidelberg-Berlin 1981.

[2] I. Chajda, Normally presented varieties, Algebra Universalis 34 (1995), 327-335.

[3] I. Chajda and K. Gazek, A Basic Course on General Algebra, TechnicalUniversity Press, Zielona Góra 2000.

[4] G. Grätzer, Universal Algebra (2nd edition), Springer-Verlag, New York-Heidelberg-Berlin 1979.

[5] B. Jónsson and E. Nelson, Relatively free products in regular varieties, Algebra Universalis 4 (1974), 14-19.

[6] H. Lakser, R. Padmanabhan and C.R. Platt, Subdirect decomposition of Płonka sums, Duke Math. J. 39 (1972), 485-488.

[7] R. McKenzie, G. McNulty and W. Taylor, Algebras, Lattices, Varieties, vol. 1, Wadsworth Brooks/Cole Advanced Books Software, Monterey, California 1987.

[8] J. Płonka, On a method of construction of abstract algebras, Fund. Math. 61 (1967), 183-189.

[9] J. Płonka, On equational classes of abstract algebras defined by regular equations, Fund. Math. 64 (1969), 241-247.

[10] J. Płonka, Biregular and uniform identities of bisemilattices, Demonstratio Math. 20 (1987), 95-107.

[11] J. Płonka, On varieties of algebras defined by identities of some special forms, Houston J. Math. 14 (1988), 253-263.

[12] J. Płonka, Biregular and uniform identities of algebras, Czechoslovak Math. J. 40 (115) (1990), 367-387.

[13] J. Płonka, Subdirect decompositions of algebras from 2-clone extension of varieties, Colloq. Math 77 (1998), 189-199.

[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.

[16] J. Płonka, On sums of direct systems of Boolean algebras, Colloq. Math. 20 (1969), 209-214.

[17] J. Płonka, Lattices of subvarieties of the clone extension of some varieties, Contributions to General Algebra 11 (1999), 161-171.

[18] J. Płonka, Clone networks, clone extensions and biregularizations of varieties of algebras, Algebra Colloq. 8 (2001), 327-344.

[19] J. Płonka. and Z. Szylicka, Subdirectly irreducible generalized sums of upper semilattice ordered systems of algebras, Algebra Universalis (in print).