ITBM-Constructive Completions of Algebras

We introduce the notion of ITBM-constructive algebra, which is a generalization of the notion of constructive algebra, and study completions of such algebras. We obtain some criterion for the existence of completions for metrized algebras and prove that each ITBM-constructive metrized algebra which...

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Bibliographic Details
Published in:	Siberian mathematical journal Vol. 65; no. 3; pp. 589 - 598
Main Author:	Morozov, A. S.
Format:	Journal Article
Language:	English
Published:	Moscow Pleiades Publishing 01-05-2024 Springer Nature B.V
Subjects:	Algebra Mathematics Mathematics and Statistics completion computability over the reals metrized algebra ITBM-constructive algebra 510.5 Blum–Shub–Smale machine generalized computability
Online Access:	Get full text
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Summary:	We introduce the notion of ITBM-constructive algebra, which is a generalization of the notion of constructive algebra, and study completions of such algebras. We obtain some criterion for the existence of completions for metrized algebras and prove that each ITBM-constructive metrized algebra which has completion can be naturally extended to the ITBM-constructive completion. Using these results, we establish the existence of ITBM-constructive presentations for some particular algebras.
ISSN:	0037-4466 1573-9260
DOI:	10.1134/S003744662403008X