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Independence in \(\ell\)-groups. (English) Zbl 0959.06008
The paper under review deals with independence and linear independence in lattice ordered groups (\(l\)-groups). The author introduces and studies new types of independences which are not included in known general schemes, but which are essential for the theory of \(l\)-groups. Characterizations and classifications of subsets of \(l\)-groups satisfying some independences introduced in the paper are obtained.
MSC:
06F15 Ordered groups
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References:
[1] Fuchs L.: Partially ordered algebraic systems. Pergamon Press, New York, 1963. · Zbl 0137.02001
[2] Kurosh A. G.: Theory of groups. Moscow, 1967. · Zbl 0189.30801
[3] Marczewski E.: A general scheme of the notions of independence in mathematics. Bull. Acad. Polon. Sci. 6 (1958), 731-736. · Zbl 0088.03001
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