On a homogeneity condition for $MV$-algebras
Czechoslovak Mathematical Journal, Tome 56 (2006) no. 1, pp. 79-98 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 06D35
Keywords: $MV$-algebra; generalized cardinal property; projectability; orthogonal completeness; direct product
@article{CMJ_2006_56_1_a6,
     author = {Jakub{\'\i}k, J\'an},
     title = {On a homogeneity condition for $MV$-algebras},
     journal = {Czechoslovak Mathematical Journal},
     pages = {79--98},
     year = {2006},
     volume = {56},
     number = {1},
     mrnumber = {2206288},
     zbl = {1164.06314},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2006_56_1_a6/}
}
TY  - JOUR
AU  - Jakubík, Ján
TI  - On a homogeneity condition for $MV$-algebras
JO  - Czechoslovak Mathematical Journal
PY  - 2006
SP  - 79
EP  - 98
VL  - 56
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/CMJ_2006_56_1_a6/
LA  - en
ID  - CMJ_2006_56_1_a6
ER  - 
%0 Journal Article
%A Jakubík, Ján
%T On a homogeneity condition for $MV$-algebras
%J Czechoslovak Mathematical Journal
%D 2006
%P 79-98
%V 56
%N 1
%U http://geodesic.mathdoc.fr/item/CMJ_2006_56_1_a6/
%G en
%F CMJ_2006_56_1_a6
Jakubík, Ján. On a homogeneity condition for $MV$-algebras. Czechoslovak Mathematical Journal, Tome 56 (2006) no. 1, pp. 79-98. http://geodesic.mathdoc.fr/item/CMJ_2006_56_1_a6/

[1] S. J.  Bernau: Lateral and Dedekind completion of archimedean lattice groups. J.  London Math. Soc. 12 (1976), 320–322. | DOI | MR | Zbl

[2] R.  Cignoli, I. M. I.  D’Ottaviano, and D.  Mundici: Algebraic Foundations of Many-Valued Reasoning. Kluwer Academic Publishers, Dordrecht, 2000. | MR

[3] P. F.  Conrad: Lateral completion of lattice ordered groups. Proc. London Math. Soc. 19 (1969), 444–480. | DOI | MR

[4] A.  Dvurečenskij, S.  Pulmannová: New Trends in Quantum Structures. Kluwer Academic Publishers and Ister Science, Dordrecht and Bratislava, 2000. | MR

[5] J.  Jakubík: Cardinal properties of lattice ordered groups. Fundamenta Math. 74 (1972), 85–98. | DOI | MR

[6] J.  Jakubík: Orthogonal hull of a strongly projectable lattice ordered group. Czechoslovak Math.  J. 28 (1978), 484–504. | MR

[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

[9] J.  Jakubík: On archimedean $MV$-algebras. Czechoslovak Math.  J. 48 (1998), 575–582. | DOI | MR

[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

[12] J.  Jakubík: On the $\alpha $-completeness of pseudo $MV$-algebras. Math. Slovaca 52 (2002), 511–516. | MR

[13] J.  Jakubík: Generalized cardinal properties of lattices and lattice ordered groups. Czechoslovak Math.  J 54 (2004), 1035–1053. | DOI | MR

[14] R. S.  Pierce: Some questions about complete Boolean-algebras. Proc. Sympos. Pure Math. 2 (1961), 129–140. | MR | Zbl

[15] E. C.  Weinberg: Higher degrees of distributivity in lattices of continuous functions. Trans. Amer. Math. Soc. 104 (1962), 334–346. | DOI | MR | Zbl

[16] W. A.  Luxemburg, A. C.  Zaanen: Riesz Spaces, Vol.  1. North Holland, Amsterdam, 1971.