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Effectively completely decomposable Abelian groups. (English. Russian original) Zbl 1042.20510

Sib. Math. J. 38, No. 6, 1227-1229 (1997); translation from Sib. Mat. Zh. 38, No. 6, 1410-1412 (1997).
Summary: We introduce the concept of complete decomposability of Abelian groups and find a criterion for the effective complete decomposability of a group \(G\) which is the direct sum of groups \(\mathbb{Q}_{p_i}\), \(i\in\mathbb{N}\), where \(p_i\) is a prime number, and \(\mathbb{Q}_p\) is an additive group of rational numbers whose denominators are powers of \(p\).

MSC:

20K25 Direct sums, direct products, etc. for abelian groups
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References:

[1] A. I. Mal’tsev, ”On recursive Abelian groups,” Dokl. Akad. Nauk SSSR,146, No. 5, 1009–1012 (1962).
[2] L. Fuchs, Infinite Abelian Groups, Vol. 1 [Russian translation], Mir, Moscow (1977). · Zbl 0366.20037
[3] H. Rogers, Theory of Recursive Functions and Effective Computability [Russian translation], Mir, Moscow (1972).
[4] Yu. L. Ershov, Decidability Problems and Constructive Models [in Russian], Nauka, Moscow (1980).
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