Free ℓ -groups and free products of ℓ -groups

Dao Rong Tong

Commentationes Mathematicae Universitatis Carolinae (1994)

  • Volume: 35, Issue: 4, page 617-625
  • ISSN: 0010-2628

Abstract

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

How to cite

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Tong, Dao Rong. "Free $\ell $-groups and free products of $\ell $-groups." Commentationes Mathematicae Universitatis Carolinae 35.4 (1994): 617-625. <http://eudml.org/doc/247617>.

@article{Tong1994,
abstract = {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 $\mathcal \{U\}$ of $i\ell $-groups. We have proved that the $\mathcal \{U\}$-free products satisfy the weak subalgebra property.},
author = {Tong, Dao Rong},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {lattice-ordered group ($\ell $-group); free $\ell $-group; free product of $\ell $-groups; sub-product class of $\ell $-groups; free l-groups; po-group; free products; weak subalgebra property},
language = {eng},
number = {4},
pages = {617-625},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Free $\ell $-groups and free products of $\ell $-groups},
url = {http://eudml.org/doc/247617},
volume = {35},
year = {1994},
}

TY - JOUR
AU - Tong, Dao Rong
TI - Free $\ell $-groups and free products of $\ell $-groups
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1994
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 35
IS - 4
SP - 617
EP - 625
AB - 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 $\mathcal {U}$ of $i\ell $-groups. We have proved that the $\mathcal {U}$-free products satisfy the weak subalgebra property.
LA - eng
KW - lattice-ordered group ($\ell $-group); free $\ell $-group; free product of $\ell $-groups; sub-product class of $\ell $-groups; free l-groups; po-group; free products; weak subalgebra property
UR - http://eudml.org/doc/247617
ER -

References

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  2. Conrad P., Lattice-Ordered Groups, Tulane Lecture Notes, Tulane University, 1970. Zbl1058.06019
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  11. Powell W.B., Tsinakis C., Free products in the class of abelian ℓ -groups, Pacific J. Math. 104 (1983), 429-442. (1983) MR0684301
  12. Powell W.B., Tsinakis C., The distributive lattice free products as a sublattice of the abelian ℓ -group free product, J. Austral. Math. Soc. 34 (1993), 92-100. (1993) MR0683181
  13. Powell W.B., Tsinakis C., Free products of lattice-ordered groups, Algebra Universalis 18 (1984), 178-198. (1984) Zbl0545.06007MR0743466
  14. Powell W.B., Tsinakis C., Disjointness conditions for free products of ℓ -groups, Arkiv. der Math. 46 (1986), 491-498. (1986) Zbl0578.06012MR0849853
  15. Powell W.B., Tsinakis C., Disjoint sets in free products of representable ℓ -groups, Proc. A.M.S. 104 (1988), 1014-1020. (1988) MR0931736
  16. Dao-Rong Ton, Free weak Hamiltonian ℓ -groups, Northeast Mathematics 10 (2) (1994), 235-240. (1994) 
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  18. Weinberg E.C., Free lattice-ordered abelian groups II, Math. Ann. 159 (1965), 217-222. (1965) Zbl0138.26201MR0181668

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