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Sib. Èlektron. Mat. Izv., 2019, Volume 16, Pages 983–997 (Mi semr1109)  

Mathematical logic, algebra and number theory

On the ascending and descending chain conditions in the lattice of monoid varieties

S. V. Gusev

Ural Federal University, Institute of Natural Sciences and Mathematics 51, Lenina ave., Ekaterinburg, 620000, Russia

Abstract: In this work we consider monoids as algebras with an associative binary operation and the nullary operation that fixes the identity element. We found an example of two varieties of monoids with finite subvariety lattices such that their join covers one of them and has a continuum cardinality subvariety lattice that violates the ascending chain condition and the descending chain condition.

Keywords: monoid, variety, lattice of varieties, ascending chain condition, descending chain condition.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 1.6018.2017/8.9
Russian Foundation for Basic Research 17-01-00551_
The work is supported by the Ministry of Education and Science of the Russian Federation (project 1.6018.2017/8.9) and by Russian Foundation for Basic Research (grant 17-01-00551).


DOI: https://doi.org/10.33048/semi.2019.16.067

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Bibliographic databases:

UDC: 512.532.2
MSC: 20M07, 08B15
Received February 13, 2019, published August 5, 2019
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Citation: S. V. Gusev, “On the ascending and descending chain conditions in the lattice of monoid varieties”, Sib. Èlektron. Mat. Izv., 16 (2019), 983–997

Citation in format AMSBIB
\Bibitem{Gus19}
\by S.~V.~Gusev
\paper On the ascending and descending chain conditions in the lattice of monoid varieties
\jour Sib. \`Elektron. Mat. Izv.
\yr 2019
\vol 16
\pages 983--997
\mathnet{http://mi.mathnet.ru/semr1109}
\crossref{https://doi.org/10.33048/semi.2019.16.067}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000479063900001}


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