Bipartite pseudo MV-algebras

Grzegorz Dymek

Discussiones Mathematicae - General Algebra and Applications (2006)

  • Volume: 26, Issue: 2, page 183-197
  • ISSN: 1509-9415

Abstract

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A bipartite pseudo MV-algebra A is a pseudo MV-algebra such that A = M ∪ M ̃ for some proper ideal M of A. This class of pseudo MV-algebras, denoted BP, is investigated. The class of pseudo MV-algebras A such that A = M ∪ M ̃ for all maximal ideals M of A, denoted BP₀, is also studied and characterized.

How to cite

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Grzegorz Dymek. "Bipartite pseudo MV-algebras." Discussiones Mathematicae - General Algebra and Applications 26.2 (2006): 183-197. <http://eudml.org/doc/276955>.

@article{GrzegorzDymek2006,
abstract = {A bipartite pseudo MV-algebra A is a pseudo MV-algebra such that A = M ∪ M ̃ for some proper ideal M of A. This class of pseudo MV-algebras, denoted BP, is investigated. The class of pseudo MV-algebras A such that A = M ∪ M ̃ for all maximal ideals M of A, denoted BP₀, is also studied and characterized.},
author = {Grzegorz Dymek},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {pseudo MV-algebra; (maximal) ideal; bipartite pseudo MV-algebra; maximal ideal},
language = {eng},
number = {2},
pages = {183-197},
title = {Bipartite pseudo MV-algebras},
url = {http://eudml.org/doc/276955},
volume = {26},
year = {2006},
}

TY - JOUR
AU - Grzegorz Dymek
TI - Bipartite pseudo MV-algebras
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2006
VL - 26
IS - 2
SP - 183
EP - 197
AB - A bipartite pseudo MV-algebra A is a pseudo MV-algebra such that A = M ∪ M ̃ for some proper ideal M of A. This class of pseudo MV-algebras, denoted BP, is investigated. The class of pseudo MV-algebras A such that A = M ∪ M ̃ for all maximal ideals M of A, denoted BP₀, is also studied and characterized.
LA - eng
KW - pseudo MV-algebra; (maximal) ideal; bipartite pseudo MV-algebra; maximal ideal
UR - http://eudml.org/doc/276955
ER -

References

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  1. [1] R. Ambrosio and A. Lettieri, A classification of bipartite MV-algebras, Math. Japonica 38 (1993), 111-117. Zbl0766.06010
  2. [2] A. Di Nola, A. Dvurečenskij and J. Jakubík, Good and bad infinitesimals, and states on pseudo MV-algebras, Order 21 (2004), 293-314. Zbl1081.06010
  3. [3] A. Di Nola, F. Liguori and S. Sessa, Using maximal ideals in the classification of MV-algebras, Port. Math. 50 (1993), 87-102. Zbl0799.06021
  4. [4] G. Dymek and A. Walendziak, On maximal ideals of GMV-algebras, submitted. 
  5. [5] G. Georgescu and A. Iorgulescu, Pseudo-MV algebras, Multi. Val. Logic. 6 (2001), 95-135. Zbl1014.06008
  6. [6] J. Rachůnek, A non-commutative generalization of MV-algebras, Czechoslovak Math. J. 52 (2002), 255-273. Zbl1012.06012
  7. [7] J. Rachůnek, Radicals in non-commutative generalizations of MV-algebras, Math. Slovaca 52 (2002), 135-144. Zbl1008.06011
  8. [8] A. Walendziak, On implicative ideals of pseudo MV-algebras, Sci. Math. Jpn. 62 (2005), 281-287;{e-2005, 363-369. Zbl1086.06011

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