Isomorphisms of direct products of lattice-ordered groups
Ján Jakubík
Discussiones Mathematicae - General Algebra and Applications, Tome 24 (2004), p. 43-52 / Harvested from The Polish Digital Mathematics Library

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

Publié le : 2004-01-01
EUDML-ID : urn:eudml:doc:287643
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1074,
     author = {J\'an Jakub\'\i k},
     title = {Isomorphisms of direct products of lattice-ordered groups},
     journal = {Discussiones Mathematicae - General Algebra and Applications},
     volume = {24},
     year = {2004},
     pages = {43-52},
     zbl = {1068.06017},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1074}
}
Ján Jakubík. Isomorphisms of direct products of lattice-ordered groups. Discussiones Mathematicae - General Algebra and Applications, Tome 24 (2004) pp. 43-52. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1074/

[000] [1] R.R. Appleson and L. Lovász, A characterization of cancellable k-ary structures, Period. Math. Hungar. 6 (1975), 17-19. | Zbl 0306.08001

[001] [2] P. Conrad, Lattice-Ordered Groups, Tulane University, New Orleans, LA, 1970. | Zbl 0258.06011

[002] [3] P. Conrad and M.R. Darnel, Lattice-ordered groups whose lattices determine their additions, Trans. Amer. Math. Soc. 330 (1992), 575-598. | Zbl 0756.06009

[003] [4] P.F. Conrad and M.R. Darnel, Generalized Boolean algebras in lattice-ordered groups, Order 14 (1998), 295-319. | Zbl 0919.06009

[004] [5] P.F. Conrad and M.R. Darnel, Subgroups and hulls of Specker lattice-ordered groups, Czechoslovak Math. J. 51 (126) (2001), 395-413. | Zbl 0978.06011

[005] [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. | Zbl 1024.06003

[006] [7] W. Hanf, On some fundamental problems concerning isomorphisms of Boolean algebras, Math. Scand. 5 (1957), 205-217. | Zbl 0081.26101

[007] [8] J. Jakubí k, Cantor-Bernstein theorem for lattice-ordered groups, Czechoslovak Math. J. 22 (97) (1972), 159-175.

[008] [9] J. Jakubí k, Direct product decompositions of infinitely distributive lattices, Math. Bohemica 125 (2000), 341-354. | Zbl 0967.06004

[009] [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.

[010] [11] J. Jakubí k, Cantor-Bernstein theorem for lattices, Math. Bohemica 127 (2002), 463-471. | Zbl 1007.06005

[011] [12] J. Jakubí k, Torsion classes of Specker lattice-ordered groups, Czechoslovak Math. J. 52 (127) (2002), 469-482.

[012] [13] J. Jakubí k, On orthogonally s-complete lattice-ordered groups, Czechoslovak Math. J. 52 (127) (2002), 881-888.

[013] [14] D. Jakubí ková-Studenovská, On a cancellation law for monounary algebras, Math. Bohemica 128 (2003), 77-90.

[014] [15] L. Lovász, Operations with structures, Acta Math. Acad. Sci. Hungar. 18 (1967), 321-328. | Zbl 0174.01401

[015] [16] L. Lovász, On the cancellation among finite relational structures, Period. Math. Hungar. 1 (1971), 145-156. | Zbl 0223.08002

[016] [17] R. McKenzie, Cardinal multiplication of structures with a reflexive relation, Fund. Math. 70 (1971), 59-101. | Zbl 0228.08002

[017] [18] R. McKenzie, G. McNulty and W. Taylor, Algebras, Lattices, Varieties, Vol. 1, Wadsworth and Brooks/Cole, Montrey, CA, 1987. | Zbl 0611.08001

[018] [19] J. Novotný, On the characterization of a certain class of monounary algebras, Math. Slovaca 40 (1990), 123-126. | Zbl 0734.08003

[019] [20] M. Ploscica and M. Zelina, Cancellation among finite unary algebras, Discrete Math. 159 (1996), 191-198.

[020] [21] R. Sikorski, A generalization of theorem of Banach and Cantor-Bernstein, Colloq. Math. 1 (1948), 140-144. | Zbl 0037.31801

[021] [22] R. Sikorski, Boolean Algebras, Second Edition, Springer-Verlag, Berlin 1964.

[022] [23] A. Tarski, Cardinal Algebras, Oxford Univ. Press, New York 1949.