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
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/
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[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).