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.
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).
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
\Bibitem{KraSch20}
\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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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
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