Normalization of M V -algebras

Ivan Chajda; Radomír Halaš; Jan Kühr; Alena Vanžurová

Mathematica Bohemica (2005)

  • Volume: 130, Issue: 3, page 283-300
  • ISSN: 0862-7959

Abstract

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We consider algebras determined by all normal identities of M V -algebras, i.e. algebras of many-valued logics. For such algebras, we present a representation based on a normalization of a sectionally involutioned lattice, i.e. a q -lattice, and another one based on a normalization of a lattice-ordered group.

How to cite

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Chajda, Ivan, et al. "Normalization of $MV$-algebras." Mathematica Bohemica 130.3 (2005): 283-300. <http://eudml.org/doc/249601>.

@article{Chajda2005,
abstract = {We consider algebras determined by all normal identities of $MV$-algebras, i.e. algebras of many-valued logics. For such algebras, we present a representation based on a normalization of a sectionally involutioned lattice, i.e. a $q$-lattice, and another one based on a normalization of a lattice-ordered group.},
author = {Chajda, Ivan, Halaš, Radomír, Kühr, Jan, Vanžurová, Alena},
journal = {Mathematica Bohemica},
keywords = {$MV$-algebra; abelian lattice-ordered group; $q$-lattice; normalization of a variety; abelian lattice-ordered group; -lattice; normalization of a variety},
language = {eng},
number = {3},
pages = {283-300},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Normalization of $MV$-algebras},
url = {http://eudml.org/doc/249601},
volume = {130},
year = {2005},
}

TY - JOUR
AU - Chajda, Ivan
AU - Halaš, Radomír
AU - Kühr, Jan
AU - Vanžurová, Alena
TI - Normalization of $MV$-algebras
JO - Mathematica Bohemica
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 130
IS - 3
SP - 283
EP - 300
AB - We consider algebras determined by all normal identities of $MV$-algebras, i.e. algebras of many-valued logics. For such algebras, we present a representation based on a normalization of a sectionally involutioned lattice, i.e. a $q$-lattice, and another one based on a normalization of a lattice-ordered group.
LA - eng
KW - $MV$-algebra; abelian lattice-ordered group; $q$-lattice; normalization of a variety; abelian lattice-ordered group; -lattice; normalization of a variety
UR - http://eudml.org/doc/249601
ER -

References

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  1. Lattice-ordered groups. An Introduction, D. Reidel., Dordrecht, 1988. (1988) MR0937703
  2. 10.1090/S0002-9947-1958-0094302-9, Trans. Amer. Math. Soc. 88 (1958), 467–490. (1958) Zbl0084.00704MR0094302DOI10.1090/S0002-9947-1958-0094302-9
  3. A new proof of the Łukasziewicz axioms, Trans. Amer. Math. Soc. 93 (1959), 74–80. (1959) MR0122718
  4. Free lattice-ordered abelian groups and varieties of M V -algebras, Proc. IX. Latin. Amer. Symp. Math. Logic, Part 1, Not. Log. Mat. 38 (1993), 113–118. (1993) Zbl0827.06012MR1332526
  5. Algebraic Foundations of Many- Valued Reasoning, Kluwer, Dordrecht, 2000. (2000) MR1786097
  6. Lattices in quasiordered sets, Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 31 (1992), 6–12. (1992) Zbl0773.06002MR1212600
  7. Congruence properties of algebras in nilpotent shifts of varieties, General Algebra and Discrete Mathematics (K. Denecke, O. Lüders, eds.), Heldermann, Berlin, 1995, pp. 35–46. (1995) Zbl0821.08009MR1336150
  8. 10.1007/BF01182089, Algebra Universalis 34 (1995), 327–335. (1995) Zbl0842.08007MR1350845DOI10.1007/BF01182089
  9. Algebras presented by normal identities, Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 38 (1999), 49–58. (1999) MR1767191
  10. Distributive lattices with sectionally antitone involutions, (to appear). (to appear) MR2160352
  11. Nilpotent shifts of varieties, Math. Notes 14 (1973), 692–696. (Russian) (1973) MR0366782
  12. 10.1016/0022-1236(86)90015-7, J. Funct. Anal. 65 (1986), 15–63. (1986) Zbl0597.46059MR0819173DOI10.1016/0022-1236(86)90015-7
  13. M V -algebras are categorically equivalent to bouded commutative B C K - algebras, Math. Japon. 31 (1986), 889–894. (1986) MR0870978
  14. M V -algebras are categorically equivalent to a class of D R l 1 ( i ) -semigroups, Math. Bohem. 123 (1998), 437–441. (1998) MR1667115

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