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

top
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

top

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

top
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.