Normalization of basic algebras

• Autorzy: Miroslav Kolařík
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

basic algebra; section antitone involution; q-lattice; normalization of a variety

Kategorie tematyczne

• 06B05: Structure theory
• 03G25: Other algebras related to logic
• 06D35: MV-algebras

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2008
• Tom: 28
• Numer: 2
• Strony: 237-249

Daty

wydano

2008

otrzymano

2008-04-10

poprawiono

2008-04-29

Twórcy

autor

Miroslav Kolařík

• Department of Computer Science, Palacký University Olomouc, Tomkova 40, 779 00 Olomouc, Czech Republic

Bibliografia

• [1] I. Chajda, Lattices in quasiordered sets, Acta Univ. Palacki. Olomuc., Fac. Rerum. Nat., Math. 31 (1992), 6-12.
• [2] 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.
• [3] I. Chajda, Normally presentable varieties, Algebra Universalis 34 (1995), 327-335.
• [4] I. Chajda and E. Graczyńska, Algebras presented by normal identities, Acta Univ. Palacki. Olomuc., Fac. Rerum. Nat., Math. 38 (1999), 49-58.
• [5] I. Chajda, R. Halaš and J. Kühr, Many-valued quantum algebras, Algebra Universalis, DOI 10.1007/s00012-008-2086-9.
• [6] I. Chajda, R. Halaš and J. Kühr, Semilattice Structures, Heldermann Verlag (Lemgo, Germany), 2007, ISBN 978-3-88538-230-0.
• [7] I. Chajda, R. Halaš, J. Kühr and A. Vanžurová, Normalization of MV-algebras, Mathematica Bohemica 130 (2005), 283-300.
• [8] I. Chajda and M. Kolařík, Independence of axiom system of basic algebras, Soft Computing, DOI 10.1007/s00500-008-0291-2.
• [9] I. Mel'nik, Nilpotent shifts of varieties, Math. Notes 14 (1973), 692-696 (in Russian).

Identyfikatory

DOI

10.7151/dmgaa.1146