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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2020, Volume 17, Pages 753–768
DOI: https://doi.org/10.33048/semi.2020.17.054 (Mi semr1248) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Mathematical logic, algebra and number theory

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

A. V. Kravchenkoabcd, M. V. Schwidefskyabd

a Sobolev Institute of Mathematics, 4, Koptyuga ave., Novosibirsk, 630090, Russia
b Novosibirsk State University, 1, Pirogova str., Novosibirsk, 630090, Russia
c Siberian Institute of Management, 6, Nizhegorodskaya str., Novosibirsk, 630102, Russia
d Novosibirsk State Technical University, 20, Karl Marx ave.., Novosibirsk, 630073, Russia
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DOI: https://doi.org/10.33048/semi.2020.17.054
Abstract: 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.
Keywords: quasivariety, variety, congruence lattice, differential groupoid, unary algebra, undecidable problem, computable set.
Funding agency Grant number
Russian Science Foundation 19-11-00209
Ministry of Science and Higher Education of the Russian Federation 0314-2019-0003
This research was carried out within the framework of the state contract of the Sobolev Institute of Mathematics, project no. 0314-2019-0003. This work is also partially supported by the RSF, project no. 19-11-00209, (statements 14–16).
Received November 19, 2019, published June 4, 2020
Bibliographic databases:
Document Type: Article
UDC: 512.57
MSC: 08C15, 03C05
Language: English
Citation: A. V. Kravchenko, M. V. Schwidefsky, “On the complexity of the lattices of subvarieties and congruences. II. Differential groupoids and unary algebras”, Sib. Èlektron. Mat. Izv., 17 (2020), 753–768
Citation in format AMSBIB
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\by A.~V.~Kravchenko, M.~V.~Schwidefsky
\paper On the complexity of the lattices of subvarieties and congruences. II. Differential groupoids and unary algebras
\jour Sib. \`Elektron. Mat. Izv.
\yr 2020
\vol 17
\pages 753--768
\mathnet{http://mi.mathnet.ru/semr1248}
\crossref{https://doi.org/10.33048/semi.2020.17.054}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000537775800001}
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    • This publication is cited in the following 7 articles:
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