Previous |  Up |  Next


pseudo $MV$-algebra; convex chain; Archimedean property; direct product decomposition
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.
[1] R.  Cignoli, M. I.  D’Ottaviano and D.  Mundici: Algebraic Foundations of Many-Valued Reasoning, Trends in Logic, Studia Logica Library, vol.  7. Kluwer Academic Publishers, Dordrecht, 2000. MR 1786097
[2] P.  Conrad: Lattice Ordered Groups. Tulane University, 1970. Zbl 0258.06011
[3] A.  Dvurečenskij and S.  Pulmannová: New Trends in Quantum Structures. Kluwer Academic Publishers, Dordrecht, and Ister Science, Bratislava, 2000. MR 1861369
[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
[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
[6] J.  Jakubík: Direct product of $MV$-algebras. Czechoslovak Math.  J. 44(119) (1994), 725–739. MR 1295146
[7] J.  Jakubík: Direct product decompositions of pseudo $MV$-algebras. Arch. Math. 37 (2001), 131–142. MR 1838410
[8] J.  Jakubík: On chains in $MV$-algebras. Math. Slovaca 51 (2001), 151–166. MR 1841444
[9] J.  Rachůnek: A non-commutative generalization of $MV$-algebras. Czechoslovak Math.  J. 52(127) (2002), 255–273. DOI 10.1023/A:1021766309509 | MR 1905434
Partner of
EuDML logo