Decomposability and computability

B. Khoussainov^ab, A. G. Melnikov<sup>cd

a</sup> Univ. Auckland, Auckland, NEW ZEALAND
^b Algorithms and Logic Lab, UESTC, Chengdu, CHINA
^c Victoria Univ. Wellington, Wellington, NEW ZEALAND
^d Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: We present a new construction of indecomposable type $\mathbf{0}$ Abelian groups of rank $2$. The new construction is used to study degree spectra of such groups. As a corollary, we obtain a new computability-theoretic proof showing that there exist continuum many nonisomorphic type $\mathbf{0}$ indecomposable Abelian groups of rank $2$.

Keywords: indecomposable type $\mathbf{0}$ Abelian groups of rank $2$.

UDC: 510.5+512.541

Received: 21.10.2021
Revised: 01.09.2022

DOI: 10.33048/alglog.2022.61.205

 English version: Algebra and Logic, 2022, 61:2, 153–159