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Free i-Groups and vector lattices

Published online by Cambridge University Press:  09 April 2009

Roger D. Bleier
Roger D. Bleier
Affiliation:
University of TexasAustin, Texas 78712, U. S. A.
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The purpose of this paper is to present three somewhat disparate results on free objects in three different classes of λ-groups. The first is that no proper ideal of a finitely generated free vector lattice can itself be a free vector lattice. Second, each free abelian lgroup is characteristically simple. The third result is that each disjoint subset of a free (non-abelian) lgroup is countable.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 19 , Issue 3 , May 1975 , pp. 337 - 342
Copyright
Copyright © Australian Mathematical Society 1975

References

Amemiya, I. (1966), ‘Countable decomposability of vector lattices’, J. Fac. Hokkaido Univ. 19, 111–113.Google Scholar
Baker, K. (1968), ‘Free vector lattices’, Canad. J. Math. 20, 58–66.Google Scholar
Bernau, S. (1969), ‘Free abelian lattice-ordered groups’, Math. Ann. 180, 48–59.CrossRefGoogle Scholar
Bleier, R., ‘Free vector lattices’, Trans. Amer. Math. Soc. 176, 73–87.CrossRefGoogle Scholar
Conrad, P., (1971) ‘Free abelian l-groups and vector lattices’, Math. Ann. 190, 306–312.CrossRefGoogle Scholar
Conrad, P. (1970), Lattice Ordered Groups. (Tulane University, New Orleans (1970)).Google Scholar
Fuchs, L. (1970), Infinite Abelian Groups. (Academic Press, New York (1970)).Google Scholar
Henriksen, M. and Isbell, J. (1962), ‘Lattice-ordered rings and function rings’, Pacific J. Math. 12, 341–364.Google Scholar
Weinberg, E.. ‘Free lattice-ordered abelian groups’, Math. Ann. 151, 187–199.Google Scholar