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

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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 9 scientific papers (total in 9 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. Kravchenko^abcd, M. V. Schwidefsky^abd

^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

Full-text PDF (200 kB) Citations (9)

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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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\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}

Linking options:

https://www.mathnet.ru/eng/semr1248

https://www.mathnet.ru/eng/semr/v17/p753

This publication is cited in the following 9 articles:

M. V. Schwidefsky, “Existence of Independent Quasi-Equational Bases. II”, Algebra Logic, 2024
M. V. Schwidefsky, “The complexity of quasivariety lattices. II”, Sib. elektron. matem. izv., 20:1 (2023), 501–513
M. V. Shvidefski, “O suschestvovanii nezavisimykh bazisov kvazitozhdestv. II”, Algebra i logika, 62:6 (2023), 762–785
A. V. Kravchenko, M. V. Schwidefsky, “On nonstandard quasivarieties of differential groupoids and unary algebras”, Sib. elektron. matem. izv., 19:2 (2022), 768–783
Kira Adaricheva, Jennifer Hyndman, J. B. Nation, Joy N. Nishida, CMS/CAIMS Books in Mathematics, 3, A Primer of Subquasivariety Lattices, 2022, 1
A. V. Kravchenko, A. M. Nurakunov, M. V. Schwidefsky, “Structure of quasivariety lattices. IV. Nonstandard quasivarieties”, Siberian Math. J., 62:5 (2021), 850–858
A. V. Kravchenko, A. M. Nurakunov, M. V. Schwidefsky, “Structure of quasivariety lattices. III. Finitely partitionable bases”, Algebra and Logic, 59:3 (2020), 222–229
M. V. Schwidefsky, “On a class of subsemigroup lattices”, Siberian Math. J., 61:5 (2020), 941–952
Schwidefsky V M., “on Sufficient Conditions For Q-Universality”, Sib. Electron. Math. Rep., 17 (2020), 1043–1051

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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