TY - JOUR

T1 - Lower Semilattices of Separable Congruences of Numbered Algebras

AU - Kasymov, N. Kh

AU - Morozov, A. S.

N1 - The first author was supported by the development program of the Scientific and Education Mathematical Center of Kazan (Volga Region) Federal University (Agreement 075–02–2022–882). The second author was also supported by the Ministry of Science and Higher Education of the Russian Federation (Project FWNF–2022–0012). Публикация для корректировки.

PY - 2023/7

Y1 - 2023/7

N2 - Under study are the closure properties for various classes of separable congruences(in particular, of equivalences)of numbered algebras on the natural numbersunder the upper and lower bounds in the lattice of congruences.We show that the class of all positive congruences forms a sublatticewhereas the classes of negative, computably separable, and separable congruences forma lower but not always an upper subsemilattice.It is shown that uniformly computably separable congruences can fail to formlower and upper semilattices.We give a characterization of semienumerable sets in terms of uniformlycomputably separable equivalences.

AB - Under study are the closure properties for various classes of separable congruences(in particular, of equivalences)of numbered algebras on the natural numbersunder the upper and lower bounds in the lattice of congruences.We show that the class of all positive congruences forms a sublatticewhereas the classes of negative, computably separable, and separable congruences forma lower but not always an upper subsemilattice.It is shown that uniformly computably separable congruences can fail to formlower and upper semilattices.We give a characterization of semienumerable sets in terms of uniformlycomputably separable equivalences.

KW - 510.5

KW - computable completeness

KW - computable separability

KW - congruence lattices of numbered algebras

KW - effectively separable congruences

KW - negative

KW - numbered algebras and morphisms

KW - positive

KW - separability

KW - uniformly computably separable congruences

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85165583657&origin=inward&txGid=b63c77a2cb8d30916809b4bd8ba7e45b

UR - https://www.mendeley.com/catalogue/330e1b0b-ee51-349d-90e4-a768f22bda7e/

U2 - 10.1134/S0037446623040080

DO - 10.1134/S0037446623040080

M3 - Article

VL - 64

SP - 864

EP - 876

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 4

ER -