ArticleOriginal scientific text
Title
Normalization of basic algebras
Authors 1
Affiliations
- Department of Computer Science, Palacký University Olomouc, Tomkova 40, 779 00 Olomouc, Czech Republic
Abstract
We consider algebras determined by all normal identities of basic algebras. For such algebras, we present a representation based on a q-lattice, i.e., the normalization of a lattice.
Keywords
basic algebra, section antitone involution, q-lattice, normalization of a variety
Bibliography
- I. Chajda, Lattices in quasiordered sets, Acta Univ. Palacki. Olomuc., Fac. Rerum. Nat., Math. 31 (1992), 6-12.
- I. Chajda, Congruence properties of algebras in nilpotent shifts of varieties, pp. 35-46 in: General Algebra and Discrete Mathematics (K. Denecke, O. Lüders, eds.), Heldermann, Berlin 1995.
- I. Chajda, Normally presentable varieties, Algebra Universalis 34 (1995), 327-335.
- I. Chajda and E. Graczyńska, Algebras presented by normal identities, Acta Univ. Palacki. Olomuc., Fac. Rerum. Nat., Math. 38 (1999), 49-58.
- I. Chajda, R. Halaš and J. Kühr, Many-valued quantum algebras, Algebra Universalis, DOI 10.1007/s00012-008-2086-9.
- I. Chajda, R. Halaš and J. Kühr, Semilattice Structures, Heldermann Verlag (Lemgo, Germany), 2007, ISBN 978-3-88538-230-0.
- I. Chajda, R. Halaš, J. Kühr and A. Vanžurová, Normalization of MV-algebras, Mathematica Bohemica 130 (2005), 283-300.
- I. Chajda and M. Kolařík, Independence of axiom system of basic algebras, Soft Computing, DOI 10.1007/s00500-008-0291-2.
- I. Mel'nik, Nilpotent shifts of varieties, Math. Notes 14 (1973), 692-696 (in Russian).