Bipartite pseudo MV-algebras

• Autorzy: Grzegorz Dymek
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

pseudo MV-algebra; (maximal) ideal; bipartite pseudo MV-algebra

Kategorie tematyczne

• 06D35: MV-algebras

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2006
• Tom: 26
• Numer: 2
• Strony: 183-197

Daty

wydano

2006

otrzymano

2006-01-02

poprawiono

2006-05-09

Twórcy

autor

Grzegorz Dymek

• Institute of Mathematics and Physics, University of Podlasie, 3 Maja 54, 08-110 Siedlce, Poland

Bibliografia

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

Identyfikatory

DOI

10.7151/dmgaa.1111