TY - JOUR

T1 - Decompositions of decidable abelian groups

AU - Bazhenov, Nikolay

AU - Goncharov, Sergey

AU - Melnikov, Alexander

PY - 2020/2/1

Y1 - 2020/2/1

N2 - 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.

AB - 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.

KW - Abelian group

KW - computable categoricity

KW - computable model theory

KW - decidable structure

KW - degree of categoricity

UR - http://www.scopus.com/inward/record.url?scp=85079275334&partnerID=8YFLogxK

U2 - 10.1142/S0218196719500644

DO - 10.1142/S0218196719500644

M3 - Article

AN - SCOPUS:85079275334

VL - 30

SP - 49

EP - 90

JO - International Journal of Algebra and Computation

JF - International Journal of Algebra and Computation

SN - 0218-1967

IS - 1

ER -