Decompositions of decidable abelian groups

Decompositions of decidable abelian groups Full article

Journal

International Journal of Algebra and Computation
ISSN: 0218-1967 , E-ISSN: 1793-6500

Output data

Year: 2020, Volume: 30, Number: 1, Pages: 49-90 Pages count : 42 DOI: 10.1142/S0218196719500644

Tags

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

Authors

Bazhenov N. ^1,2 , Goncharov S. ^1,2 , Melnikov A. ³

Affiliations

1	Sobolev Institute of Mathematics, Akad. Koptyug Ave. 4, Novosibirsk, 630090, Russian Federation
2	Novosibirsk State University, 2 Pirogova St., Novosibirsk, 630090, Russian Federation
3	Massey University Auckland, Private Bag 102904, North Shore, Auckland, 0745, New Zealand

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. © 2020 World Scientific Publishing Company.

Bazhenov N. , Goncharov S. , Melnikov A.
Decompositions of decidable abelian groups
International Journal of Algebra and Computation. 2020. V.30. N1. P.49-90. DOI: 10.1142/S0218196719500644 WOS Scopus OpenAlex

Web of science:	WOS:000514097000003
Scopus:	2-s2.0-85079275334
OpenAlex:	W2970632373

DB	Citing
Scopus	3
OpenAlex	3
Web of science	2