Normalization of basic algebras

Miroslav Kolařík

Discussiones Mathematicae - General Algebra and Applications (2008)

  • Volume: 28, Issue: 2, page 237-249
  • ISSN: 1509-9415

Abstract

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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.

How to cite

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Miroslav Kolařík. "Normalization of basic algebras." Discussiones Mathematicae - General Algebra and Applications 28.2 (2008): 237-249. <http://eudml.org/doc/276847>.

@article{MiroslavKolařík2008,
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.},
author = {Miroslav Kolařík},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {basic algebra; section antitone involution; q-lattice; normalization of a variety; -lattice},
language = {eng},
number = {2},
pages = {237-249},
title = {Normalization of basic algebras},
url = {http://eudml.org/doc/276847},
volume = {28},
year = {2008},
}

TY - JOUR
AU - Miroslav Kolařík
TI - Normalization of basic algebras
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2008
VL - 28
IS - 2
SP - 237
EP - 249
AB - 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.
LA - eng
KW - basic algebra; section antitone involution; q-lattice; normalization of a variety; -lattice
UR - http://eudml.org/doc/276847
ER -

References

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  1. [1] I. Chajda, Lattices in quasiordered sets, Acta Univ. Palacki. Olomuc., Fac. Rerum. Nat., Math. 31 (1992), 6-12. Zbl0773.06002
  2. [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. Zbl0821.08009
  3. [3] I. Chajda, Normally presentable varieties, Algebra Universalis 34 (1995), 327-335. 
  4. [4] I. Chajda and E. Graczyńska, Algebras presented by normal identities, Acta Univ. Palacki. Olomuc., Fac. Rerum. Nat., Math. 38 (1999), 49-58. Zbl0993.08002
  5. [5] I. Chajda, R. Halaš and J. Kühr, Many-valued quantum algebras, Algebra Universalis, DOI 10.1007/s00012-008-2086-9. Zbl1219.06013
  6. [6] I. Chajda, R. Halaš and J. Kühr, Semilattice Structures, Heldermann Verlag (Lemgo, Germany), 2007, ISBN 978-3-88538-230-0. 
  7. [7] I. Chajda, R. Halaš, J. Kühr and A. Vanžurová, Normalization of MV-algebras, Mathematica Bohemica 130 (2005), 283-300. Zbl1112.06012
  8. [8] I. Chajda and M. Kolařík, Independence of axiom system of basic algebras, Soft Computing, DOI 10.1007/s00500-008-0291-2. Zbl1178.06007
  9. [9] I. Mel'nik, Nilpotent shifts of varieties, Math. Notes 14 (1973), 692-696 (in Russian). 

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