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

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

Journal

Сибирские электронные математические известия (Siberian Electronic Mathematical Reports)
, E-ISSN: 1813-3304

Output data

Year: 2020, Volume: 17, Pages: 753-768 Pages count : 16 DOI: 10.33048/SEMI.2020.17.054

Tags

Computable set; Congruence lattice; Differential groupoid; Quasivariety; Unary algebra; Undecidable problem; Variety

Authors

Kravchenko A.V. ^1,2,3,4 , Schwidefsky M.V. ^1,2,4

Affiliations

1	Sobolev Institute of Mathematics, 4, Koptyuga ave., Novosibirsk, 630090, Russia
2	Novosibirsk State University, 1, Pirogova str., Novosibirsk, 630090, Russia
3	Siberian Institute of Management, 6, Nizhegorodskaya str., Novosibirsk, 630102, Russian Federation
4	Novosibirsk State Technical University, 20, Karl Marx ave., Novosibirsk, 630073, Russia

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.

Kravchenko A.V. , Schwidefsky M.V.
On the complexity of the lattices of subvarieties and congruences. II. Differential groupoids and unary algebras
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2020. V.17. P.753-768. DOI: 10.33048/SEMI.2020.17.054 WOS Scopus OpenAlex

Web of science:	WOS:000537775800001
Scopus:	2-s2.0-85089221682
OpenAlex:	W3036815777

DB	Citing
Scopus	7
OpenAlex	6
Web of science	7