FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2007, VOLUME 13, NUMBER 3, PAGES 209-221

On subdirect sums of Abelian torsion-free groups of rank $1$

V. B. Trukhmanov

Abstract

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In this paper, we study torsion-free Abelian groups of rank $2$, which are subdirect sums of two divisible rational groups, with the inducing group $$Q/Z. The class of special groups is defined and investigated. It is shown that there is a one-to-one correspondence between the set of all special groups and the multiplicative group of unity elements of the ring of universal numbers.

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Last modified: June 19, 2007