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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1111,
author = {Grzegorz Dymek},
title = {Bipartite pseudo MV-algebras},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {26},
year = {2006},
pages = {183-197},
zbl = {1130.06006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1111}
}
Grzegorz Dymek. Bipartite pseudo MV-algebras. Discussiones Mathematicae - General Algebra and Applications, Tome 26 (2006) pp. 183-197. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1111/
[000] [1] R. Ambrosio and A. Lettieri, A classification of bipartite MV-algebras, Math. Japonica 38 (1993), 111-117. | Zbl 0766.06010
[001] [2] A. Di Nola, A. Dvurečenskij and J. Jakubík, Good and bad infinitesimals, and states on pseudo MV-algebras, Order 21 (2004), 293-314. | Zbl 1081.06010
[002] [3] A. Di Nola, F. Liguori and S. Sessa, Using maximal ideals in the classification of MV-algebras, Port. Math. 50 (1993), 87-102. | Zbl 0799.06021
[003] [4] G. Dymek and A. Walendziak, On maximal ideals of GMV-algebras, submitted.
[004] [5] G. Georgescu and A. Iorgulescu, Pseudo-MV algebras, Multi. Val. Logic. 6 (2001), 95-135. | Zbl 1014.06008
[005] [6] J. Rachůnek, A non-commutative generalization of MV-algebras, Czechoslovak Math. J. 52 (2002), 255-273. | Zbl 1012.06012
[006] [7] J. Rachůnek, Radicals in non-commutative generalizations of MV-algebras, Math. Slovaca 52 (2002), 135-144. | Zbl 1008.06011
[007] [8] A. Walendziak, On implicative ideals of pseudo MV-algebras, Sci. Math. Jpn. 62 (2005), 281-287;{e-2005, 363-369. | Zbl 1086.06011