Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
lattice ordered group; orthogonal $\sigma $-completeness; direct factor
lattice ordered group; orthogonal $\sigma $-completeness; direct factor
Summary:
In this paper we prove a theorem of Cantor-Bernstein type for orthogonally $\sigma $-complete lattice ordered groups.
References:
[1] J. Jakubík: Cardinal properties of lattice ordered groups. Fund. Math. 74 (1972), 85–98. DOI 10.4064/fm-74-2-85-98 | MR 0302528
[2] J. Jakubík: Cantor-Bernstein theorem for lattice ordered groups. Czechoslovak Math. J. 22(97) (1972), 159–175. MR 0297666
[3] J. Jakubík: On complete lattice ordered groups with strong units. Czechoslovak Math. J. 46(121) (1996), 221–230. MR 1388611
[4] J. Jakubík: Cantor-Bernstein theorem for $MV$-algebras. Czechoslovak Math. J. 49(124) (1999), 517–526. DOI 10.1023/A:1022467218309 | MR 1708370
[5] J. Jakubík: Convex isomorphisms of archimedean lattice ordered groups. Mathware Soft Comput. 5 (1998), 49–56. MR 1632739
[6] R. Sikorski: A generalization of theorem of Banach and Cantor-Bernstein. Coll. Mat. 1 (1948), 140–144. MR 0027264
[7] R. Sikorski: Boolean algebras. Second edition, Springer Verlag, Berlin, 1964. MR 0126393 | Zbl 0123.01303
[8] F. Šik: To the theory of lattice ordered groups. Czechoslovak Math. J. 6(81) (1956), 1–25. (Russian)
[9] A. De Simone, D. Mundici and M. Navara: A Cantor-Bernstein theorem for $\sigma $-complete $MV$-algebras. (Preprint).
[10] A. Tarski: Cardinal Algebras. Oxford University Press, New York, London, 1949. MR 0029954 | Zbl 0041.34502
Search
Partner of
