TY - JOUR

T1 - Profinite Locally Finite Quasivarieties

AU - Nurakunov, Anvar M.

AU - Schwidefsky, Marina V.

N1 - The authors are grateful to the referee for thorough reading the paper and many helpful comments. The second author was supported by the Russian Science Foundation, project no. 22-21-00104.

PY - 2024/8

Y1 - 2024/8

N2 - Let K and M be locally finite quasivarieties of finite type such that K⊂ M . If K is profinite then the filter [K, M] in the quasivariety lattice Lq (M) is an atomic lattice and K has an independent quasi-equational basis relative to M . Applications of these results for lattices, unary algebras, groups, unary algebras, and distributive algebras are presented which concern some well-known problems on standard topological quasivarieties and other problems.

AB - Let K and M be locally finite quasivarieties of finite type such that K⊂ M . If K is profinite then the filter [K, M] in the quasivariety lattice Lq (M) is an atomic lattice and K has an independent quasi-equational basis relative to M . Applications of these results for lattices, unary algebras, groups, unary algebras, and distributive algebras are presented which concern some well-known problems on standard topological quasivarieties and other problems.

KW - Inverse limit

KW - Locally finite

KW - Profinite structure

KW - Quasi-equational basis

KW - Quasivariety

KW - Standard quasivariety

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85174198959&origin=inward&txGid=8cd519e00ba615e3791ee2b144979178

UR - https://www.mendeley.com/catalogue/df5acda4-47ac-3a11-9edb-45ed4d1908a1/

U2 - 10.1007/s11225-023-10077-y

DO - 10.1007/s11225-023-10077-y

M3 - Article

VL - 112

SP - 835

EP - 859

JO - Studia Logica

JF - Studia Logica

SN - 0039-3215

IS - 4

ER -