Decompositions of decidable abelian groups
Nikolay A. Bazhenov, Sergey Savostyanovich Goncharov, Alexander Melnikov · International Journal of Algebra and Computation · 2019
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.