decomposable group
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2019 ◽  
Vol 30 (01) ◽  
pp. 49-90 ◽  
Author(s):  
Nikolay Bazhenov ◽  
Sergey Goncharov ◽  
Alexander Melnikov

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.


2007 ◽  
Vol 315 (2) ◽  
pp. 640-653 ◽  
Author(s):  
L.S. Kazarin ◽  
A. Martínez-Pastor ◽  
M.D. Pérez-Ramos
Keyword(s):  

1978 ◽  
Vol 23 (5) ◽  
pp. 355-359
Author(s):  
V. S. Monakhov
Keyword(s):  

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