Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
lattice ordered group; weak homogeneity; direct product; cardinal property; $f$-homogeneity
lattice ordered group; weak homogeneity; direct product; cardinal property; $f$-homogeneity
Summary:
In this paper we deal with weakly homogeneous direct factors of lattice ordered groups. The main result concerns the case when the lattice ordered groups under consideration are archimedean, projectable and conditionally orthogonally complete.
References:
[1] G. Birkhoff: Lattice Theory. Third Edition, Providence, 1967. MR 0227053 | Zbl 0153.02501
[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. Conrad: Lattice Ordered Groups. Tulane University, 1970. Zbl 0258.06011
[4] J. Jakubík: Cardinal properties of lattice ordered groups. Fundamenta Math. 74 (1972), 85–98. DOI 10.4064/fm-74-2-85-98 | MR 0302528
[5] J. Jakubík: Konvexe Ketten in $\ell $-Gruppen. Časopis pěst. mat. 83 (1958), 53–63. MR 0104740
[6] J. Jakubík: Retract mappings of projectable $MV$-algebras. Soft Computing 4 (2000), 27–32.
[7] J. Jakubík: Direct product decompositions of MV-algebras. Czech. Math. J. 44 (1994), 725–739.
[8] J. Jakubík: Weak homogeneity of and Pierce’s theorem for $MV$-algebras. Czech. Math. J. 56 (2006), 1215–1227. DOI 10.1007/s10587-006-0090-9 | MR 2280805
[9] 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
[10] R. S. Pierce: Some questions about complete Boolean algebras. Proc. Sympos. Pure Math. 2 (1961), 129–140. MR 0138570 | Zbl 0101.27104
[11] R. Sikorski: Boolean Algebras. Second Edition, Springer Verlag, Berlin, 1964. MR 0126393 | Zbl 0123.01303
[12] F. Šik: Über subdirekte Summen geordneter Gruppen. Czech. Math. J. 10 (1960), 400–424. MR 0123626
Search
Partner of
