On subdirect sums of Abelian torsion-free groups of rank 1
Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 3, pp. 209-221
Cet article a éte moissonné depuis la source Math-Net.Ru
In this paper, we study torsion\df free Abelian groups of rank 2, which are subdirect sums of two divisible rational groups, with the inducing group $\mathbb{Q}/\mathbb{Z}$. 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.
@article{FPM_2007_13_3_a19,
author = {V. B. Trukhmanov},
title = {On subdirect sums of {Abelian} torsion-free groups of rank~1},
journal = {Fundamentalʹna\^a i prikladna\^a matematika},
pages = {209--221},
year = {2007},
volume = {13},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_2007_13_3_a19/}
}
V. B. Trukhmanov. On subdirect sums of Abelian torsion-free groups of rank 1. Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 3, pp. 209-221. http://geodesic.mathdoc.fr/item/FPM_2007_13_3_a19/
[1] Kulikov L. Ya., “Podpryamye razlozheniya schetnykh abelevykh grupp bez krucheniya”, Kh Vsesoyuzn. algebr. kollokvium, Novosibirsk, 1969, 18–19
[2] Kulikov L. Ya., “O podpryamykh summakh abelevykh grupp bez krucheniya pervogo ranga”, KhII Vsesoyuzn. algebr. kollokvium, Sverdlovsk, 1973, 30
[3] Fuks L., Beskonechnye abelevy gruppy, T. 1, Mir, M., 1974