ArticleOriginal scientific text

Title

Isomorphisms of direct products of lattice-ordered groups

Authors 1

Affiliations

  1. Matematický ústav SAV, Grešákova 6, 040 01 Košice, Slovakia

Abstract

In this paper we investigate sufficient conditions for the validity of certain implications concerning direct products of lattice-ordered groups.

Keywords

Lattice-ordered group, direct product, Specker lattice-ordered group, orthogonal σ-completeness

Bibliography

  1. R.R. Appleson and L. Lovász, A characterization of cancellable k-ary structures, Period. Math. Hungar. 6 (1975), 17-19.
  2. P. Conrad, Lattice-Ordered Groups, Tulane University, New Orleans, LA, 1970.
  3. P. Conrad and M.R. Darnel, Lattice-ordered groups whose lattices determine their additions, Trans. Amer. Math. Soc. 330 (1992), 575-598.
  4. P.F. Conrad and M.R. Darnel, Generalized Boolean algebras in lattice-ordered groups, Order 14 (1998), 295-319.
  5. P.F. Conrad and M.R. Darnel, Subgroups and hulls of Specker lattice-ordered groups, Czechoslovak Math. J. 51 (126) (2001), 395-413.
  6. A. De Simone, D. Mundici and M. Navara, A Cantor-Bernstein theorem for s-complete MV-algebras, Czechoslovak Math. J. 53 (128) (2003), 437-447.
  7. W. Hanf, On some fundamental problems concerning isomorphisms of Boolean algebras, Math. Scand. 5 (1957), 205-217.
  8. J. Jakubí k, Cantor-Bernstein theorem for lattice-ordered groups, Czechoslovak Math. J. 22 (97) (1972), 159-175.
  9. J. Jakubí k, Direct product decompositions of infinitely distributive lattices, Math. Bohemica 125 (2000), 341-354.
  10. J. Jakubí k, A theorem of Cantor-Bernstein type for orthogonally s-complete pseudo MV-algebras, Tatra Mt. Math. Publ. 22 (2001), 91-103.
  11. J. Jakubí k, Cantor-Bernstein theorem for lattices, Math. Bohemica 127 (2002), 463-471.
  12. J. Jakubí k, Torsion classes of Specker lattice-ordered groups, Czechoslovak Math. J. 52 (127) (2002), 469-482.
  13. J. Jakubí k, On orthogonally s-complete lattice-ordered groups, Czechoslovak Math. J. 52 (127) (2002), 881-888.
  14. D. Jakubí ková-Studenovská, On a cancellation law for monounary algebras, Math. Bohemica 128 (2003), 77-90.
  15. L. Lovász, Operations with structures, Acta Math. Acad. Sci. Hungar. 18 (1967), 321-328.
  16. L. Lovász, On the cancellation among finite relational structures, Period. Math. Hungar. 1 (1971), 145-156.
  17. R. McKenzie, Cardinal multiplication of structures with a reflexive relation, Fund. Math. 70 (1971), 59-101.
  18. R. McKenzie, G. McNulty and W. Taylor, Algebras, Lattices, Varieties, Vol. 1, Wadsworth and Brooks/Cole, Montrey, CA, 1987.
  19. J. Novotný, On the characterization of a certain class of monounary algebras, Math. Slovaca 40 (1990), 123-126.
  20. M. Ploscica and M. Zelina, Cancellation among finite unary algebras, Discrete Math. 159 (1996), 191-198.
  21. R. Sikorski, A generalization of theorem of Banach and Cantor-Bernstein, Colloq. Math. 1 (1948), 140-144.
  22. R. Sikorski, Boolean Algebras, Second Edition, Springer-Verlag, Berlin 1964.
  23. A. Tarski, Cardinal Algebras, Oxford Univ. Press, New York 1949.
Pages:
43-52
Main language of publication
English
Received
2003-07-01
Accepted
2004-01-27
Published
2004
Exact and natural sciences