# Isomorphisms of direct products of lattice-ordered groups

Discussiones Mathematicae - General Algebra and Applications (2004)

- Volume: 24, Issue: 1, page 43-52
- ISSN: 1509-9415

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topJán Jakubík. "Isomorphisms of direct products of lattice-ordered groups." Discussiones Mathematicae - General Algebra and Applications 24.1 (2004): 43-52. <http://eudml.org/doc/287643>.

@article{JánJakubík2004,

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

author = {Ján Jakubík},

journal = {Discussiones Mathematicae - General Algebra and Applications},

keywords = {Lattice-ordered group; direct product; Specker lattice-ordered group; orthogonal σ-completeness; lattice-ordered group; orthogonal -completeness},

language = {eng},

number = {1},

pages = {43-52},

title = {Isomorphisms of direct products of lattice-ordered groups},

url = {http://eudml.org/doc/287643},

volume = {24},

year = {2004},

}

TY - JOUR

AU - Ján Jakubík

TI - Isomorphisms of direct products of lattice-ordered groups

JO - Discussiones Mathematicae - General Algebra and Applications

PY - 2004

VL - 24

IS - 1

SP - 43

EP - 52

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

LA - eng

KW - Lattice-ordered group; direct product; Specker lattice-ordered group; orthogonal σ-completeness; lattice-ordered group; orthogonal -completeness

UR - http://eudml.org/doc/287643

ER -

## References

top- [1] R.R. Appleson and L. Lovász, A characterization of cancellable k-ary structures, Period. Math. Hungar. 6 (1975), 17-19. Zbl0306.08001
- [2] P. Conrad, Lattice-Ordered Groups, Tulane University, New Orleans, LA, 1970. Zbl0258.06011
- [3] P. Conrad and M.R. Darnel, Lattice-ordered groups whose lattices determine their additions, Trans. Amer. Math. Soc. 330 (1992), 575-598. Zbl0756.06009
- [4] P.F. Conrad and M.R. Darnel, Generalized Boolean algebras in lattice-ordered groups, Order 14 (1998), 295-319. Zbl0919.06009
- [5] P.F. Conrad and M.R. Darnel, Subgroups and hulls of Specker lattice-ordered groups, Czechoslovak Math. J. 51 (126) (2001), 395-413. Zbl0978.06011
- [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. Zbl1024.06003
- [7] W. Hanf, On some fundamental problems concerning isomorphisms of Boolean algebras, Math. Scand. 5 (1957), 205-217. Zbl0081.26101
- [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. Zbl0967.06004
- [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. Zbl1007.06005
- [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. Zbl0174.01401
- [16] L. Lovász, On the cancellation among finite relational structures, Period. Math. Hungar. 1 (1971), 145-156. Zbl0223.08002
- [17] R. McKenzie, Cardinal multiplication of structures with a reflexive relation, Fund. Math. 70 (1971), 59-101. Zbl0228.08002
- [18] R. McKenzie, G. McNulty and W. Taylor, Algebras, Lattices, Varieties, Vol. 1, Wadsworth and Brooks/Cole, Montrey, CA, 1987. Zbl0611.08001
- [19] J. Novotný, On the characterization of a certain class of monounary algebras, Math. Slovaca 40 (1990), 123-126. Zbl0734.08003
- [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. Zbl0037.31801
- [22] R. Sikorski, Boolean Algebras, Second Edition, Springer-Verlag, Berlin 1964.
- [23] A. Tarski, Cardinal Algebras, Oxford Univ. Press, New York 1949.

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