On free abelian $l$-groups
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- by Paul Hill PDF
- Proc. Amer. Math. Soc. 38 (1973), 53-58 Request permission
Abstract:
Let $F$ denote the free abelian lattice ordered group over an unordered torsion free group $G$. Necessary and sufficient conditions are given on $G$ in order for $F$ to be an $l$-subgroup of a cardinal product of integers. The result encompasses Weinbergโs theorem that the freeness of $G$ is sufficient. The corresponding embedding theorem for $F$ is also established whenever $G$ is completely decomposable and homogeneous.References
- S. J. Bernau, Free abelian lattice groups, Math. Ann. 180 (1969), 48โ59. MR 241340, DOI 10.1007/BF01350085
- Paul F. Conrad, Subdirect sums of integers and reals, Proc. Amer. Math. Soc. 19 (1968), 1176โ1182. MR 232721, DOI 10.1090/S0002-9939-1968-0232721-X
- L. Fuchs, Abelian groups, Publishing House of the Hungarian Academy of Sciences, Budapest, 1958. MR 0106942
- Elliot Carl Weinberg, Free lattice-ordered abelian groups. II, Math. Ann. 159 (1965), 217โ222. MR 181668, DOI 10.1007/BF01362439
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 38 (1973), 53-58
- MSC: Primary 06A60
- DOI: https://doi.org/10.1090/S0002-9939-1973-0313159-5
- MathSciNet review: 0313159