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 Zap. Nauchn. Sem. POMI, 2014, Volume 423, Pages 166–182 (Mi znsl6003)

Inherently non-finitely generated varieties of aperiodic monoids with central idempotents

Edmond W. H. Lee

Division of Math., Science, and Technology, Nova Southeastern University, 3301 College Avenue, Fort Lauderdale, Florida 33314, USA

Abstract: Let $\mathscr A$ denote the class of aperiodic monoids with central idempotents. A subvariety of $\mathscr A$ that is not contained in any finitely generated subvariety of $\mathscr A$ is said to be inherently non-finitely generated. A characterization of inherently non-finitely generated subvarieties of $\mathscr A$, based on identities that they cannot satisfy and monoids that they must contain, is given. It turns out that there exists a unique minimal inherently non-finitely generated subvariety of $\mathscr A$, the inclusion of which is both necessary and sufficient for a subvariety of $\mathscr A$ to be inherently non-finitely generated. Further, it is decidable in polynomial time if a finite set of identities defines an inherently non-finitely generated subvariety of $\mathscr A$.

Key words and phrases: monoid, aperiodic monoid, central idempotent, variety, finitely generated, inherently non-finitely generated.

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English version:
Journal of Mathematical Sciences (New York), 2015, 209:4, 588–599

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UDC: 512.5
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Citation: Edmond W. H. Lee, “Inherently non-finitely generated varieties of aperiodic monoids with central idempotents”, Problems in the theory of representations of algebras and groups. Part 26, Zap. Nauchn. Sem. POMI, 423, POMI, St. Petersburg, 2014, 166–182; J. Math. Sci. (N. Y.), 209:4 (2015), 588–599

Citation in format AMSBIB
\Bibitem{Lee14} \by Edmond~W.~H.~Lee \paper Inherently non-finitely generated varieties of aperiodic monoids with central idempotents \inbook Problems in the theory of representations of algebras and groups. Part~26 \serial Zap. Nauchn. Sem. POMI \yr 2014 \vol 423 \pages 166--182 \publ POMI \publaddr St.~Petersburg \mathnet{http://mi.mathnet.ru/znsl6003} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3480696} \transl \jour J. Math. Sci. (N. Y.) \yr 2015 \vol 209 \issue 4 \pages 588--599 \crossref{https://doi.org/10.1007/s10958-015-2515-1} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84943358523} 

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This publication is cited in the following articles:
1. S. V. Gusev, “On the lattice of overcommutative varieties of monoids”, Russian Math. (Iz. VUZ), 62:5 (2018), 23–26
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