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A SUFFICIENT CONDITION UNDER WHICH A SEMIGROUP IS NONFINITELY BASED

Part of: Semigroups

Published online by Cambridge University Press:  11 November 2015

WEN TING ZHANG  and
YAN FENG LUO
WEN TING ZHANG*
Affiliation:
School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, PR China Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou, Gansu 730000, PR China Department of Mathematics and Statistics, La Trobe University, VIC 3086, Australia email zhangwt@lzu.edu.cn
YAN FENG LUO
Affiliation:
School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, PR China Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou, Gansu 730000, PR China Department of Mathematics and Statistics, La Trobe University, VIC 3086, Australia email luoyf@lzu.edu.cn
*
✉zhangwt@lzu.edu.cn
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Abstract

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We give a sufficient condition under which a semigroup is nonfinitely based. As an application, we show that a certain variety is nonfinitely based, and we indicate the additional analysis (to be presented in a forthcoming paper), which shows that this example is a new limit variety of aperiodic monoids.

Keywords

semigroupidentityfinitely basedvariety

MSC classification

Primary: 20M07: Varieties and pseudovarieties of semigroups
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 93 , Issue 3 , June 2016 , pp. 454 - 466
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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