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On the Jakubík problem on radical classes of lattice ordered groups. (English) Zbl 0841.06015
Let \(\sigma\) be a radical class, \(A' (\sigma)\) be the class of all antiatoms over \(\sigma\) in the lattice of all radical classes \(S\) and \(\varepsilon' (\sigma)\) be the supremum of \(A' (\sigma)\). The author proves that there are \(\sigma, \tau\in S\) such that \(A' (\sigma)\neq \emptyset\), \(\sigma< \tau< \varepsilon' (\sigma)\) and \(A' (\tau)= \emptyset\).
MSC:
06F15 Ordered groups
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References:
[1] J. Jakubík: Radical mappings and radical classes of lattice ordered groups. Symposia Math. 21 (1977), 451-477.
[2] P. Conrad: Lattice-ordered groups. Tulane University, 1970. · Zbl 0258.06011
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