Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
$MV$-algebra; generalized cardinal property; projectability; orthogonal completeness; direct product
$MV$-algebra; generalized cardinal property; projectability; orthogonal completeness; direct product
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.
References:
[1] S. J. Bernau: Lateral and Dedekind completion of archimedean lattice groups. J. London Math. Soc. 12 (1976), 320–322. DOI 10.1112/jlms/s2-12.3.320 | MR 0401579 | 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. MR 1786097
[3] P. F. Conrad: Lateral completion of lattice ordered groups. Proc. London Math. Soc. 19 (1969), 444–480. DOI 10.1112/plms/s3-19.3.444 | MR 0244125
[4] A. Dvurečenskij, S. Pulmannová: New Trends in Quantum Structures. Kluwer Academic Publishers and Ister Science, Dordrecht and Bratislava, 2000. MR 1861369
[5] J. Jakubík: Cardinal properties of lattice ordered groups. Fundamenta Math. 74 (1972), 85–98. DOI 10.4064/fm-74-2-85-98 | MR 0302528
[6] J. Jakubík: Orthogonal hull of a strongly projectable lattice ordered group. Czechoslovak Math. J. 28 (1978), 484–504. MR 0505957
[7] J. Jakubík: Direct product decompositions of $MV$-algebras. Czechoslovak Math. J. 44 (1994), 725–739.
[8] J. Jakubík: On complete $MV$-algebras. Czechoslovak Math. J. 45 (1995), 473–480. MR 1344513
[9] J. Jakubík: On archimedean $MV$-algebras. Czechoslovak Math. J. 48 (1998), 575–582. DOI 10.1023/A:1022436113418 | MR 1637871
[10] J. Jakubík: Retract mappings of projectable $MV$-algebras. Soft Computing 4 (2000), 27–32.
[11] J. Jakubík: Direct product decompositions of pseudo $MV$-algebras. Archivum Math. 37 (2001), 131–142. MR 1838410
[12] J. Jakubík: On the $\alpha $-completeness of pseudo $MV$-algebras. Math. Slovaca 52 (2002), 511–516. MR 1963441
[13] J. Jakubík: Generalized cardinal properties of lattices and lattice ordered groups. Czechoslovak Math. J 54 (2004), 1035–1053. DOI 10.1007/s10587-004-6449-x | MR 2100012
[14] R. S. Pierce: Some questions about complete Boolean-algebras. Proc. Sympos. Pure Math. 2 (1961), 129–140. MR 0138570 | Zbl 0101.27104
[15] E. C. Weinberg: Higher degrees of distributivity in lattices of continuous functions. Trans. Amer. Math. Soc. 104 (1962), 334–346. DOI 10.1090/S0002-9947-1962-0138569-8 | MR 0138569 | Zbl 0105.09401
[16] W. A. Luxemburg, A. C. Zaanen: Riesz Spaces, Vol. 1. North Holland, Amsterdam, 1971.
Search
Partner of
