Previous |  Up |  Next

Article

Keywords:
$MV$-algebra; weak homogeneity; internal direct product decomposition
Summary:
In this paper we prove a theorem on weak homogeneity of $MV$-algebras which generalizes a known result on weak homogeneity of Boolean algebras. Further, we consider a homogeneity condition for $MV$-algebras which is defined by means of an increasing cardinal property.
References:
[1] R. Cignoli, I. M. I. D’Ottaviano and D. Mundici: Algebraic Foundations of Many-Valued Reasoning. Kluwer Academic Publishers, Dordrecht, 2000. MR 1786097
[2] J. Jakubík: Konvexe Ketten in $\ell $-Gruppen. Časopis pěst. mat. 84 (1959), 53–63. MR 0104740
[3] J. Jakubík: Cardinal properties of lattice ordered groups. Fundamenta Math. 74 (1972), 85–98. MR 0302528
[4] J. Jakubík: Direct product decomposition of MV-algebras. Czechoslovak Math. J. 44 (1994), 725–739. MR 1295146
[5] 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
[6] J. Jakubík: On a homogeneity condition for $MV$-algebras. Czechoslovak Math. J 56 (2006), 79–97. DOI 10.1007/s10587-006-0007-7 | MR 2206288
[7] R. S. Pierce: A note on complete Boolean algebras. Proc. Amer. Math. Soc. 9 (1958), 892–896. DOI 10.1090/S0002-9939-1958-0102487-6 | MR 0102487
[8] R. S. Pierce: Some questions about complete Boolean algebras. Proc. Sympos. Pure Math. 2 (1961), 129–140. MR 0138570 | Zbl 0101.27104
[9] R. Sikorski: Boolean Algebras. Second Edition, Springer Verlag, Berlin, 1964. MR 0126393 | Zbl 0123.01303
Partner of
EuDML logo