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Mosc. Math. J., 2012, Volume 12, Number 4, Pages 787–802 (Mi mmj482)  

This article is cited in 5 scientific papers (total in 5 papers)

Maximal Specht varieties of monoids

Edmond W. H. Lee

Division of Math., Science, and Technology, Nova Southeastern University, Fort Lauderdale, Florida 33314, USA

Abstract: A variety of algebras is a Specht variety if all its subvarieties are finitely based. This article presents the first example of a maximal Specht variety of monoids. The existence of such an example is counterintuitive since it is long known that maximal Specht varieties of semigroups do not exist. This example permits a characterization of Specht varieties in the following four classes based on identities that they must satisfy and varieties that they cannot contain: (1) overcommutative varieties, (2) varieties containing a certain monoid of order seven, (3) varieties of aperiodic monoids with central idempotents, and (4) subvarieties of the variety generated by the Brandt monoid of order six. Other results, including the uniqueness or nonexistence of limit varieties within the aforementioned four classes, are also deduced. Specifically, overcommutative limit varieties of monoids do not exist. In contrast, the limit variety of semigroups, discovered by M. V. Volkov in the 1980s, is an overcommutative variety.

Key words and phrases: Monoids, varieties, Specht varieties, limit varieties, finitely based, hereditarily finitely based.

DOI: https://doi.org/10.17323/1609-4514-2012-12-4-787-802

Full text: http://www.mathjournals.org/.../2012-012-004-008.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 20M07
Received: December 7, 2010; in revised form November 24, 2011
Language:

Citation: Edmond W. H. Lee, “Maximal Specht varieties of monoids”, Mosc. Math. J., 12:4 (2012), 787–802

Citation in format AMSBIB
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\by Edmond~W.~H.~Lee
\paper Maximal Specht varieties of monoids
\jour Mosc. Math.~J.
\yr 2012
\vol 12
\issue 4
\pages 787--802
\mathnet{http://mi.mathnet.ru/mmj482}
\crossref{https://doi.org/10.17323/1609-4514-2012-12-4-787-802}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3076856}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000314341500008}


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

    This publication is cited in the following articles:
    1. J. Math. Sci. (N. Y.), 209:4 (2015), 588–599  mathnet  crossref  mathscinet
    2. Lee E.W.H., “on Certain Cross Varieties of Aperiodic Monoids With Commuting Idempotents”, Results Math., 66:3-4 (2014), 491–510  crossref  mathscinet  zmath  isi  scopus
    3. Sapir O., “Finitely Based Monoids”, Semigr. Forum, 90:3 (2015), 587–614  crossref  mathscinet  zmath  isi  elib  scopus
    4. O. Sapir, “The finite basis problem for words with at most two non-linear variables”, Semigr. Forum, 93:1 (2016), 131–151  crossref  mathscinet  zmath  isi  scopus
    5. Gusev V S., Vernikov B.M., “Chain Varieties of Monoids”, Diss. Math., 2018, no. 534, 1–73  mathscinet  zmath  isi
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