Convex chains in a pseudo MV-algebra

Ján Jakubík

Czechoslovak Mathematical Journal (2003)

  • Volume: 53, Issue: 1, page 113-125
  • ISSN: 0011-4642

Abstract

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For a pseudo M V -algebra 𝒜 we denote by ℓ ( 𝒜 ) the underlying lattice of 𝒜 . In the present paper we investigate the algebraic properties of maximal convex chains in ℓ ( 𝒜 ) containing the element 0. We generalize a result of Dvurečenskij and Pulmannová.

How to cite

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Jakubík, Ján. "Convex chains in a pseudo MV-algebra." Czechoslovak Mathematical Journal 53.1 (2003): 113-125. <http://eudml.org/doc/30763>.

@article{Jakubík2003,
abstract = {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.},
author = {Jakubík, Ján},
journal = {Czechoslovak Mathematical Journal},
keywords = {pseudo $MV$-algebra; convex chain; Archimedean property; direct product decomposition; pseudo MV-algebra; convex chain; Archimedean property; direct product decomposition},
language = {eng},
number = {1},
pages = {113-125},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Convex chains in a pseudo MV-algebra},
url = {http://eudml.org/doc/30763},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Jakubík, Ján
TI - Convex chains in a pseudo MV-algebra
JO - Czechoslovak Mathematical Journal
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 53
IS - 1
SP - 113
EP - 125
AB - 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.
LA - eng
KW - pseudo $MV$-algebra; convex chain; Archimedean property; direct product decomposition; pseudo MV-algebra; convex chain; Archimedean property; direct product decomposition
UR - http://eudml.org/doc/30763
ER -

References

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  1. Algebraic Foundations of Many-Valued Reasoning, Trends in Logic, Studia Logica Library, vol.  7, Kluwer Academic Publishers, Dordrecht, 2000. (2000) MR1786097
  2. Lattice Ordered Groups, Tulane University, 1970. (1970) Zbl0258.06011
  3. New Trends in Quantum Structures, Kluwer Academic Publishers, Dordrecht, and Ister Science, Bratislava, 2000. (2000) MR1861369
  4. Pseudo M V -algebras: a noncommutative extension of M V -algebras, In: The Proceedings of the Fourth International Symposyium on Economic Informatics, Bucharest, 1999, pp. 961–968. (1999) MR1730100
  5. Pseudo M V -algebras, Multiple Valued Logic (a special issue dedicated to Gr. C.  Moisil) 6 (2001), 95–135. (2001) MR1817439
  6. Direct product of M V -algebras, Czechoslovak Math.  J. 44(119) (1994), 725–739. (1994) MR1295146
  7. Direct product decompositions of pseudo M V -algebras, Arch. Math. 37 (2001), 131–142. (2001) MR1838410
  8. On chains in M V -algebras, Math. Slovaca 51 (2001), 151–166. (2001) MR1841444
  9. 10.1023/A:1021766309509, Czechoslovak Math.  J. 52(127) (2002), 255–273. (2002) MR1905434DOI10.1023/A:1021766309509

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