ABOUT SUBDIRECT SUMS OF INFINITE CYCLIC ABELIAN GROUPS
TRUKHMANOV Vyacheslav Borisovich
Lobachevsky State University of Nizhni Novgorod (Branch) in Arzamas
Abstract. The article is devoted to the research of one of the subclasses of Abelian torsion-free groups class of rank 2, namely, to Abelian groups that are a subdirect sum of two infinite cyclic groups with inducing finite cyclic group (such groups are called "elementary special"). The problem of describing Abelian groups with torsion-free finite rank, different from rank 1 (for the groups of rank 1 the problem is solved), is sufficiently important and actively solved in the theory of Abelian groups. The author considers some features of the groups of this subclass.
Key words and phrases: абелева группа, абелева группа без кручения, бесконечная циклическая группа, подпрямая сумма абелевых групп, кольцо целых чисел, кольцо вычетов, Abelian group, Abelian torsion-free group, infinite cyclic group, subdirect sum of Abelian groups, ring of integers, residue ring
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