## On a homogeneity condition for MV-algebras.(English)Zbl 1164.06314

Summary: In this paper we deal with a homogeneity condition for an MV-algebra concerning a generalized cardinal property. As an application, we consider the homogeneity with respect to $$\alpha$$-completeness, where $$\alpha$$ runs over the class of all infinite cardinals.

### MSC:

 06D35 MV-algebras
Full Text:

### References:

 [1] S. J. Bernau: Lateral and Dedekind completion of archimedean lattice groups. J. London Math. Soc. 12 (1976), 320–322. · Zbl 0333.06008 [2] R. Cignoli, I. M. I. D’Ottaviano, and D. Mundici: Algebraic Foundations of Many-Valued Reasoning. Kluwer Academic Publishers, Dordrecht, 2000. · Zbl 0937.06009 [3] P. F. Conrad: Lateral completion of lattice ordered groups. Proc. London Math. Soc. 19 (1969), 444–480. · Zbl 0182.04803 [4] A. Dvurečenskij, S. Pulmannová: New Trends in Quantum Structures. Kluwer Academic Publishers and Ister Science, Dordrecht and Bratislava, 2000. [5] J. Jakubík: Cardinal properties of lattice ordered groups. Fundamenta Math. 74 (1972), 85–98. · Zbl 0259.06015 [6] J. Jakubík: Orthogonal hull of a strongly projectable lattice ordered group. Czechoslovak Math. J. 28 (1978), 484–504. · Zbl 0391.06014 [7] J. Jakubík: Direct product decompositions of MV-algebras. Czechoslovak Math. J. 44 (1994), 725–739. · Zbl 0821.06011 [8] J. Jakubík: On complete MV-algebras. Czechoslovak Math. J. 45 (1995), 473–480. · Zbl 0841.06010 [9] J. Jakubík: On archimedean MV-algebras. Czechoslovak Math. J. 48 (1998), 575–582. · Zbl 0951.06011 [10] J. Jakubík: Retract mappings of projectable MV-algebras. Soft Computing 4 (2000), 27–32. · Zbl 1005.06007 [11] J. Jakubík: Direct product decompositions of pseudo MV-algebras. Archivum Math. 37 (2001), 131–142. · Zbl 1070.06003 [12] J. Jakubík: On the {$$\alpha$$}-completeness of pseudo MV-algebras. Math. Slovaca 52 (2002), 511–516. · Zbl 1030.06009 [13] J. Jakubík: Generalized cardinal properties of lattices and lattice ordered groups. Czechoslovak Math. J 54 (2004), 1035–1053. · Zbl 1080.06029 [14] R. S. Pierce: Some questions about complete Boolean-algebras. Proc. Sympos. Pure Math. 2 (1961), 129–140. · Zbl 0101.27104 [15] E. C. Weinberg: Higher degrees of distributivity in lattices of continuous functions. Trans. Amer. Math. Soc. 104 (1962), 334–346. · Zbl 0105.09401 [16] W. A. Luxemburg, A. C. Zaanen: Riesz Spaces, Vol. 1. North Holland, Amsterdam, 1971.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.