# Article

 Title: Cantor-Bernstein theorem for lattices (English) Author: Jakubík, Ján Language: English Journal: Mathematica Bohemica ISSN: 0862-7959 Volume: 127 Issue: 3 Year: 2002 Pages: 463-471 Summary lang: English . Category: math . Summary: This paper is a continuation of a previous author’s article; the result is now extended to the case when the lattice under consideration need not have the least element. (English) Keyword: lattice Keyword: direct product decomposition Keyword: Cantor-Bernstein Theorem MSC: 06B05 idZBL: Zbl 1007.06005 idMR: MR1931330 . Date available: 2009-09-24T22:03:46Z Last updated: 2012-06-18 Stable URL: http://hdl.handle.net/10338.dmlcz/134062 . Reference: [1] A. De Simone, D. Mundici, M. Navara: A Cantor-Bernstein theorem for $\sigma$-complete $MV$-algebras.(to appear). Reference: [2] J. Jakubík: Cantor-Bernstein theorem for lattice ordered groups.Czechoslovak Math. J. 22 (1972), 159–175. MR 0297666 Reference: [3] J. Jakubík: On complete lattice ordered groups with strong units.Czechoslovak Math. J. 46 (1996), 221–230. MR 1388611 Reference: [4] J. Jakubík: Convex isomorphisms of archimedean lattice ordered groups.Mathware and Soft Computing 5 (1998), 49–56. MR 1632739 Reference: [5] J. Jakubík: Cantor-Bernstein theorem for $MV$-algebras.Czechoslovak Math. J. 49 (1999), 517–526. MR 1708370 Reference: [6] J. Jakubík: Direct product decompositions of infinitely distributive lattices.Math. Bohem. 125 (2000), 341–354. MR 1790125 Reference: [7] J. Jakubík: On orthogonally $\sigma$-complete lattice ordered groups.(to appear). MR 1940067 Reference: [8] J. Jakubík: Convex mappings of archimedean $MV$-algebras.(to appear). MR 1864107 Reference: [9] J. Jakubík: A theorem of Cantor-Bernstein type for orthogonally $\sigma$-complete pseudo $MV$-algebras.(Submitted). Reference: [10] R. Sikorski: A generalization of theorem of Banach and Cantor-Bernstein.Coll. Math. 1 (1948), 140–144. MR 0027264 Reference: [11] R. Sikorski: Boolean Algebras.Second Edition, Springer, Berlin, 1964. Zbl 0123.01303, MR 0126393 Reference: [12] E. C. Smith, jr., A. Tarski: Higher degrees of distributivity and completeness in Boolean algebras.Trans. Amer. Math. Soc. 84 (1957), 230–257. MR 0084466 Reference: [13] A. Tarski: Cardinal Algebras.New York, 1949. Zbl 0041.34502 .

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