Free $\ell $-groups and free products of $\ell $-groups
Tong, Dao Rong
Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994), p. 617-625 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

In this paper we have given the construction of free $\ell $-groups generated by a po-group and the construction of free products in any sub-product class $\Cal U$ of $i\ell$-groups. We have proved that the $\Cal U$-free products satisfy the weak subalgebra property.

Publié le : 1994-01-01
Classification:  06F15,  20F60 
@article{118703,
     author = {Dao Rong Tong},
     title = {Free $\ell $-groups and free products of $\ell $-groups},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {35},
     year = {1994},
     pages = {617-625},
     zbl = {0820.06010},
     mrnumber = {1321232},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118703}
}

Tong, Dao Rong. Free $\ell $-groups and free products of $\ell $-groups. Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) pp. 617-625. http://gdmltest.u-ga.fr/item/118703/

Anderson M.; Feil T. Lattice-Ordered Groups (An Introduction), D. Reidel Publishing Company, 1988. | MR 0937703 | Zbl 0636.06008

Conrad P. Lattice-Ordered Groups, Tulane Lecture Notes, Tulane University, 1970. | Zbl 1058.06019

Conrad P. Free lattice-ordered groups, J. of Algebra 16 (1970), 191-203. (1970) | MR 0270992 | Zbl 0213.31502

Holland W.C.; Scringer E. Free products of lattice-ordered groups, Algebra Universalis 2 (1972), 247-254. (1972) | MR 0319843

Glass A.M.W.; Holland W.C. Lattice-Ordered Groups (Advances and Techniques), Kluwer Academic Publishers, 1989. | MR 1036072 | Zbl 0705.06001

Grätzer G. Universal Algebra, 2nd ed., Springer-Verlag, New York, 1979. | MR 0538623

Martinez J. Free products in varieties of lattice-ordered groups, Czech. Math. J. 22 (1972), 535-553. (1972) | MR 0311536 | Zbl 0247.06022

Martinez J. Free products of abelian $\ell $-groups, Czech. Math. J. 23 (1973), 349-361. (1973) | MR 0371770

Martinez J. (Ed.) Ordered Algebraic Structure, Kluwer Academic Publishers, 1989, pp. 11-49. | MR 1094821

Powell W.B.; Tsinakis C. Free products of abelian $\ell $-groups are cardinally indecomposable, Proc. A.M.S. 86 (1982), 385-390. (1982) | MR 0671199

Powell W.B.; Tsinakis C. Free products in the class of abelian $\ell $-groups, Pacific J. Math. 104 (1983), 429-442. (1983) | MR 0684301

Powell W.B.; Tsinakis C. The distributive lattice free products as a sublattice of the abelian $\ell $-group free product, J. Austral. Math. Soc. 34 (1993), 92-100. (1993) | MR 0683181

Powell W.B.; Tsinakis C. Free products of lattice-ordered groups, Algebra Universalis 18 (1984), 178-198. (1984) | MR 0743466 | Zbl 0545.06007

Powell W.B.; Tsinakis C. Disjointness conditions for free products of $\ell $-groups, Arkiv. der Math. 46 (1986), 491-498. (1986) | MR 0849853 | Zbl 0578.06012

Powell W.B.; Tsinakis C. Disjoint sets in free products of representable $\ell $-groups, Proc. A.M.S. 104 (1988), 1014-1020. (1988) | MR 0931736

Dao-Rong Ton Free weak Hamiltonian $\ell $-groups, Northeast Mathematics 10 (2) (1994), 235-240. (1994)

Weinberg E.C. Free lattice-ordered abelian groups, Math. Ann. 151 (1963), 187-199. (1963) | MR 0153759 | Zbl 0114.25801

Weinberg E.C. Free lattice-ordered abelian groups II, Math. Ann. 159 (1965), 217-222. (1965) | MR 0181668 | Zbl 0138.26201