Some mixed abelian groups as modules over the ring of pseudo—rational numbers

Modules over the ring of pseudorational numbers and quotient divisible groups

“…In [2] it was proved that the class of quotient divisible groups with locally free generalized characteristic coincides with the well-known class G of self-small groups of finite torsion and free rank, which was introduced by Glaz and Wickless in [6].…”

“…The ring of pseudorational numbers and modules over this ring were introduced by Fomin in [2] and Krylov in [12,13]. Later, in [3,4] Fomin applied such modules to the study of quotient divisible mixed groups and torsion free groups of finite rank.…”

“…Besides [2], modules over the ring of pseudorational numbers were treated in [14], where the injective modules were described, and in [13], where the ideals of the ring of pseudorational numbers were described and some questions about endomorphism rings and groups of homomorphisms for sp-groups were answered. This paper can be divided into three parts.…”

“…We shall also use some other rings introduced in the papers [2] and [13]. Let χ = (m p ) be an arbitrary characteristic, and let…”

“…The following properties of the rings R χ were obtained in [2]. Properties: Next we consider some invariants of modules over the ring of pseudorational numbers and recall some properties of such modules.…”