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Title: Convex chains in a pseudo MV-algebra (English)
Author: Jakubík, Ján
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 53
Issue: 1
Year: 2003
Pages: 113-125
Summary lang: English
Category: math
Summary: For a pseudo $MV$-algebra $\mathcal A$ we denote by $\ell (\mathcal A)$ the underlying lattice of $\mathcal A$. In the present paper we investigate the algebraic properties of maximal convex chains in $\ell (\mathcal A)$ containing the element 0. We generalize a result of Dvurečenskij and Pulmannová. (English)
Keyword: pseudo $MV$-algebra
Keyword: convex chain
Keyword: Archimedean property
Keyword: direct product decomposition
MSC: 06D35
idZBL: Zbl 1014.06010
idMR: MR1962003
Date available: 2009-09-24T10:59:43Z
Last updated: 2020-07-03
Stable URL:
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Reference: [2] P.  Conrad: Lattice Ordered Groups.Tulane University, 1970. Zbl 0258.06011
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Reference: [4] G.  Georgescu and A.  Iorgulescu: Pseudo $MV$-algebras: a noncommutative extension of $MV$-algebras.In: The Proceedings of the Fourth International Symposyium on Economic Informatics, Bucharest, 1999, pp. 961–968. MR 1730100
Reference: [5] G.  Georgescu and A.  Iorgulescu: Pseudo $MV$-algebras.Multiple Valued Logic (a special issue dedicated to Gr. C.  Moisil) 6 (2001), 95–135. MR 1817439
Reference: [6] J.  Jakubík: Direct product of $MV$-algebras.Czechoslovak Math.  J. 44(119) (1994), 725–739. MR 1295146
Reference: [7] J.  Jakubík: Direct product decompositions of pseudo $MV$-algebras.Arch. Math. 37 (2001), 131–142. MR 1838410
Reference: [8] J.  Jakubík: On chains in $MV$-algebras.Math. Slovaca 51 (2001), 151–166. MR 1841444
Reference: [9] J.  Rachůnek: A non-commutative generalization of $MV$-algebras.Czechoslovak Math.  J. 52(127) (2002), 255–273. MR 1905434, 10.1023/A:1021766309509


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