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Algebraic classes of Abelian torsion-free and lattice-ordered groups. (English) Zbl 0591.20057

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.

MSC:

20K40 Homological and categorical methods for abelian groups
20K20 Torsion-free groups, infinite rank
06F20 Ordered abelian groups, Riesz groups, ordered linear spaces
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