Hager, Anthony W.; Madden, James J. Algebraic classes of Abelian torsion-free and lattice-ordered groups. (English) Zbl 0591.20057 Bull. Greek Math. Soc. 25, 53-63 (1984). Summary: It is more-or-less known, that, in abelian torsion-free or lattice- ordered groups, if P is a set of prime numbers, then the class of P- divisible groups is closed under formation of products, pure subgroups, and quotients - we say, an \(HS_ EP\)-class - and that the associated subcategory is full, epireflective, and quotient closed - we say, an algebraic subcategory. This paper proves the converses: Any nontrivial \(HS_ EP\)-class (resp., algebraic subcategory) is the class (resp., subcategory) of P-divisible groups, for some set P of primes. Cited in 4 Documents MSC: 20K40 Homological and categorical methods for abelian groups 20K20 Torsion-free groups, infinite rank 06F20 Ordered abelian groups, Riesz groups, ordered linear spaces Keywords:torsion-free Abelian groups; lattice-ordered groups; P-divisible groups PDFBibTeX XMLCite \textit{A. W. Hager} and \textit{J. J. Madden}, Bull. Greek Math. Soc. 25, 53--63 (1984; Zbl 0591.20057) Full Text: EuDML