PDF
Discussiones Mathematicae General Algebra and Applications 24(1) (2004) 43-52
DOI: https://doi.org/10.7151/dmgaa.1074
ISOMORPHISMS OF DIRECT PRODUCTS OF LATTICE-ORDERED GROUPS
Ján Jakubík
Matematický ústav SAV
Gresákova 6, 040 01 Kosice, Slovakia
e-mail: kstefan@saske.sk
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 s-completeness.
2000 Mathematics Subject Classification: 06F15.
References
| [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. |
| [23] | R. Sikorski, Boolean Algebras, Second Edition, Springer-Verlag, Berlin 1964. |
| [24] | A. Tarski, Cardinal Algebras, Oxford Univ. Press, New York 1949. |
Received 1 July 2003
Revised 27 January 2004
Close