Decompositions of decidable abelian groups

Nikolay Bazhenov, Sergey Goncharov, Alexander Melnikov

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


We use computability-theoretic tools to measure the complexity of the process of direct decomposing an abelian group based on its symbolic presentation. More specifically, we compare degrees of decidable categoricity of abelian groups with degrees of categoricity of their natural direct summands. As a nontrivial and unexpected application of our methods, we show that every decidable copy of a nondivisible homogeneous completely decomposable group has an algorithm for linear independence.

Original languageEnglish
Pages (from-to)49-90
Number of pages42
JournalInternational Journal of Algebra and Computation
Issue number1
Publication statusPublished - 1 Feb 2020


  • Abelian group
  • computable categoricity
  • computable model theory
  • decidable structure
  • degree of categoricity


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