Geodesic
Horizontal sums of basic algebras
Discussiones Mathematicae. General Algebra and Applications, Tome 29 (2009) no. 1, pp. 21-33.

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The variety of basic algebras is closed under formation of horizontal sums. We characterize when a given basic algebra is a horizontal sum of chains, MV-algebras or Boolean algebras.
Keywords: Basic algebra, horizontal sum, chain basic algebra, MV-algebra, Boolean algebra 
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Chajda, Ivan. Horizontal sums of basic algebras. Discussiones Mathematicae. General Algebra and Applications, Tome 29 (2009) no. 1, pp. 21-33. http://geodesic.mathdoc.fr/item/DMGAA_2009_29_1_a1/

[1] I. Chajda, Lattices and semilattices having an antitone involution in every upper interval, Comment. Math. Univ. Carolinae 44 (2003), 577-585.

[2] I. Chajda, R. Halaš and J. Kühr, Semilattice Structures, Heldermann Verlag, Lemgo (Germany), 2007, 228pp, ISBN 978-3-88538-230-0.

[3] I. Chajda, R. Halaš and J. Kühr, Many-valued quantum algebras, Algebra Universalis 60 (2009), 63-90. %DOI 10.1007/s00012-008-2086-9.

[4] I. Chajda and H. Länger, A characterization of horizontal sums of Boolean rings, Contributions to General Algebra 18, Proceedings of the conference Arbeitstagung Allgemeine Algebra 73, Klagenfurt 2007, Verlag J. Heyn, Klagenfurt (2007), 23-30.

[5] A. Dvurečenskij and S. Pulmannová, New Trends in Quantum Structures, Kluwer Acad. Publ., Dordrecht 2000.

[6] D.J. Foulis and M.K. Bennett, Effect algebras and unsharp quantum logic, Found. Phys. 24 (1994), 1325-1346.

[7] Z. Riečanová, Generalization of blocks for D-lattices and lattice-ordered effect algebras, Intern. J. Theor. Phys. 39 (2000), 231-237.

[8] N. Vaserstein, Non-commutative number theory, Contemp. Math. 83 (1989), 445-449