Open AccessSeparable Algorithmic Representations of Classical Systems and Their Applications
Author(s) -
N. Kh. Kasymov,
R. N. Dadazhanov,
F. N. Ibragimov
Publication year - 2021
Publication title -
sovremennaâ matematika. fundamentalʹnye napravleniâ
Language(s) - English
Resource type - Journals
eISSN - 2949-0618
pISSN - 2413-3639
DOI - 10.22363/2413-3639-2021-67-4-707-754
Subject(s) - separable space , embedding , algebraic number , hierarchy , algebra over a field , mathematics , computer science , pure mathematics , theoretical computer science , artificial intelligence , mathematical analysis , economics , market economy
The main results of the theory of separable algorithmic representations of classical algebraic systems are presented. The most important classes of such systems and their representations in the lower classes of the arithmetic hierarchy - positive and negative - are described. Special attention is paid to the algorithmic, structural and topological properties of separable representations of groups, rings and bodies, as well as to effective analogs of the Maltsev theorem on embedding rings in bodies. The possibilities of using the studied concepts in the framework of theoretical informatics are considered.