Cross varieties of aperiodic monoids with central idempotents

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

FINITELY GENERATED LIMIT VARIETIES OF APERIODIC MONOIDS WITH CENTRAL IDEMPOTENTS

2009 ◽  
Vol 08 (06) ◽  
pp. 779-796 ◽  
Author(s):  
EDMOND W. H. LEE
Keyword(s):  
Present Article ◽  
Variety Of Algebras ◽  
Finitely Based ◽  
Finitely Generated ◽  
Finitely Based Variety ◽  
Limit Variety ◽  
Aperiodic Monoids

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.

THE DOT-DEPTH OF A GENERATING CLASS OF APERIODIC MONOIDS IS COMPUTABLE

1992 ◽  
Vol 03 (04) ◽  
pp. 419-442 ◽  
Author(s):  
F. BLANCHET-SADRI
Keyword(s):  
Natural Extension ◽  
Finite Alphabet ◽  
Aperiodic Monoids ◽  
Positive Integers

Given a finite alphabet A and a sequence of positive integers [Formula: see text] congruences on A*, denoted by [Formula: see text] and related to a version of the Ehrenfeucht-Fraïssé game, have been defined by Thomas in order to give a new proof that the Brzozowski’s dot-depth hierarchy of star-free languages is infinite. A natural extension of some of the results of Thomas states that the monoid variety corresponding to level k of the Straubing hierarchy (the Straubing hierarchy is closely related to the Brzozowski’s dot-depth hierarchy) can be characterized in terms of the monoids [Formula: see text]. In this paper, it is shown that the dot-depth of the [Formula: see text]’s is computable.

scholarly journals Reduction algorithms for some classes of aperiodic monoids

1985 ◽  
Vol 19 (3) ◽  
pp. 233-260 ◽  
Author(s):  
Roman König
Keyword(s):  
Aperiodic Monoids

A SUFFICIENT CONDITION UNDER WHICH A SEMIGROUP IS NONFINITELY BASED

2015 ◽  
Vol 93 (3) ◽  
pp. 454-466
Author(s):  
WEN TING ZHANG ◽  
YAN FENG LUO
Keyword(s):  
Forthcoming Paper ◽  
Additional Analysis ◽  
Sufficient Condition ◽  
Limit Variety ◽  
Aperiodic Monoids ◽  
Nonfinitely Based

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.

scholarly journals A PROFINITE APPROACH TO STABLE PAIRS

2010 ◽  
Vol 20 (02) ◽  
pp. 269-285 ◽  
Author(s):  
KARSTEN HENCKELL ◽  
JOHN RHODES ◽  
BENJAMIN STEINBERG
Keyword(s):  
Short Proof ◽  
Finite Monoids ◽  
Aperiodic Monoids ◽  
Stable Pairs

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.

scholarly journals Programs over aperiodic monoids

1989 ◽  
Vol 64 (3) ◽  
pp. 271-280 ◽  
Author(s):  
Denis Therien
Keyword(s):  
Aperiodic Monoids

A SURVEY ON SMALL FRAGMENTS OF FIRST-ORDER LOGIC OVER FINITE WORDS

2008 ◽  
Vol 19 (03) ◽  
pp. 513-548 ◽  
Author(s):  
VOLKER DIEKERT ◽  
PAUL GASTIN ◽  
MANFRED KUFLEITNER
Keyword(s):  
Algebraic Approach ◽  
Order Logic ◽  
First Order Logic ◽  
First Order ◽  
Restricted Number ◽  
Aperiodic Monoids

We consider fragments of first-order logic over finite words. In particular, we deal with first-order logic with a restricted number of variables and with the lower levels of the alternation hierarchy. We use the algebraic approach to show decidability of expressibility within these fragments. As a byproduct, we survey several characterizations of the respective fragments. We give complete proofs for all characterizations and we provide all necessary background. Some of the proofs seem to be new and simpler than those which can be found elsewhere. We also give a proof of Simon's theorem on factorization forests restricted to aperiodic monoids because this is simpler and sufficient for our purpose.

scholarly journals Limit varieties of aperiodic monoids with commuting idempotents

2020 ◽  
pp. 2150160
Author(s):  
S. V. Gusev
Keyword(s):  
Variety Of Algebras ◽  
Finitely Based ◽  
Aperiodic Monoids ◽  
Nonfinitely Based

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.

Inherently Non-Finitely Generated Varieties of Aperiodic Monoids with Central Idempotents

2015 ◽  
Vol 209 (4) ◽  
pp. 588-599 ◽  
Author(s):  
E. W. H. Lee
Keyword(s):  
Finitely Generated ◽  
Aperiodic Monoids

On Certain Cross Varieties of Aperiodic Monoids with Commuting Idempotents

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