On the complexity of the lattices of subvarieties and congruences. II. Differential groupoids and unary algebras | Zendy

A. V. Kravchenko | Zendy; М. V. Schwidefsky | Zendy

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On the complexity of the lattices of subvarieties and congruences. II. Differential groupoids and unary algebras

Author(s) -

A. V. Kravchenko,

М. V. Schwidefsky

Publication year - 2020

Publication title -

sibirskie elektronnye matematicheskie izvestiya

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.468

H-Index - 11

ISSN - 1813-3304

DOI - 10.33048/semi.2020.17.054

Subject(s) - unary operation , congruence relation , mathematics , pure mathematics , differential (mechanical device) , algebra over a field , discrete mathematics , physics , thermodynamics

We prove that certain lattices can be represented as the lattices of relative subvarieties and relative congruences of differential groupoids and unary algebras. This representation result implies that there are continuum many quasivarieties of differential groupoids such that the sets of isomorphism types of finite sublattices of their lattices of relative subvarieties and congruences are not computable. A similar result is obtained for unary algebras and their lattices of relative congruences.

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