aperiodic monoids
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Author(s):  
S. V. Gusev

A variety of algebras is called limit if it is nonfinitely-based but all its proper subvarieties are finitely-based. A monoid is aperiodic if all its subgroups are trivial. We classify all limit varieties of aperiodic monoids with commuting idempotents.



2019 ◽  
Vol 234 (1) ◽  
pp. 451-498 ◽  
Author(s):  
Samuel J. van Gool ◽  
Benjamin Steinberg


2015 ◽  
Vol 93 (3) ◽  
pp. 454-466
Author(s):  
WEN TING ZHANG ◽  
YAN FENG LUO

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.





2014 ◽  
Vol 66 (3-4) ◽  
pp. 491-510 ◽  
Author(s):  
Edmond W. H. Lee
Keyword(s):  


2012 ◽  
Vol 86 (1) ◽  
pp. 212-220 ◽  
Author(s):  
Wen Ting Zhang




2011 ◽  
pp. 425-429 ◽  
Author(s):  
Edmond W.  H. Lee
Keyword(s):  


2010 ◽  
Vol 20 (02) ◽  
pp. 269-285 ◽  
Author(s):  
KARSTEN HENCKELL ◽  
JOHN RHODES ◽  
BENJAMIN STEINBERG

We give a short proof, using profinite techniques, that idempotent pointlikes, stable pairs and triples are decidable for the pseudovariety of aperiodic monoids. Stable pairs are also described for the pseudovariety of all finite monoids.



2009 ◽  
Vol 08 (06) ◽  
pp. 779-796 ◽  
Author(s):  
EDMOND W. H. LEE

A non-finitely based variety of algebras is said to be a limit variety if all its proper subvarieties are finitely based. Recently, Marcel Jackson published two examples of finitely generated limit varieties of aperiodic monoids with central idempotents and questioned whether or not they are unique. The present article answers this question affirmatively.



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