zbMATH — the first resource for mathematics

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 \(A' (\tau)= \emptyset\).
06F15 Ordered groups
Full Text: EuDML
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.