TY - JOUR

T1 - ITBM-Constructive Completions of Algebras

AU - Morozov, A. S.

N1 - The author was supported by the Russian Science Foundation grant no. 23\u201311\u201300170, https://rscf.ru/project/23-11-00170/.

PY - 2024/5

Y1 - 2024/5

N2 - 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.

AB - 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.

KW - 510.5

KW - Blum–Shub–Smale machine

KW - ITBM-constructive algebra

KW - completion

KW - computability over the reals

KW - generalized computability

KW - metrized algebra

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85195148580&origin=inward&txGid=3ed8eb04ca4df0ed3d92409100b62b46

UR - https://www.mendeley.com/catalogue/4153f2bc-9448-381e-9ee8-0a798b8f5bda/

U2 - 10.1134/S003744662403008X

DO - 10.1134/S003744662403008X

M3 - Article

VL - 65

SP - 589

EP - 598

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 3

ER -