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On the equation V∗G=EV

J. Almeida, A. Escada
2002 Journal of Pure and Applied Algebra  
Subpseudovarieties V of DS are considered, including all subpseudovarieties of LI; DA; DS itself, and J, the latter providing a new proof of a result of Henckell and Rhodes.  ...  This note uses some recent powerful tools related with semidirect products V * W of pseudovarieties of semigroups, particularly when the second factor is the pseudovariety G of all ÿnite groups, to give  ...  EDA = DA * G. Proof. By [2], the pseudovariety DA is local. Hence, by Corollary 3.6, DA * G is deÿned by the pseudoidentities of the form (( ) ! ) 2 = ( ) !  ... 
doi:10.1016/s0022-4049(01)00010-x fatcat:riqf2vizrjeyplrdxvlhdlgrii

SOME OPERATORS THAT PRESERVE THE LOCALITY OF A PSEUDOVARIETY OF SEMIGROUPS

ALFREDO COSTA, ANA ESCADA
2013 International journal of algebra and computation  
It is shown that if V is a local monoidal pseudovariety of semigroups, then K(m)V, D(m)V and LI(m)V are local. Other operators of the form Z(m)(_) are considered.  ...  In the process, results about the interplay between operators Z(m)(_) and (_)*D_k are obtained.  ...  In [13, 14] one finds some unary operators preserving the locality of subpseudovarieties of the pseudovariety DS of monoids whose regular D-classes are semigroups.  ... 
doi:10.1142/s0218196713500112 fatcat:6jvwzr4rmbewpa2w4tai7k2gty

PROFINITE METHODS IN SEMIGROUP THEORY

PASCAL WEIL
2002 International journal of algebra and computation  
Important results started owing rapidly, and there are at present a number of surveys and basic references, some dated 3, 111] and some still very useful, notably Almeida's book 5] but also 21, 17].  ...  A highlight of the Conference held at the University of Nebraska-Lincoln in May 2000 was the proof of the decidability of the complexity of nite semigroups and automata, presented by Rhodes 78].  ...  direct product of a group and a rectangular band) 29], Almeida 6 ] and Trotter and Weil 109] on DA (the aperiodic semigroups in DS), Costa 34] on many subpseudovarieties of DO, etc.  ... 
doi:10.1142/s0218196702000912 fatcat:nbautgyhrjcwpajcehfgb2bgyy

Infinite-vertex free profinite semigroupoids and symbolic dynamics

Jorge Almeida, Alfredo Costa
2009 Journal of Pure and Applied Algebra  
This is done with examples of free profinite semigroupoids generated by the graph of a subshift.  ...  Some fundamental questions about infinite-vertex (free) profinite semigroupoids are clarified, putting in evidence differences with the finitevertex case.  ...  Let D the set of letters d of A such that {γ ∈ β | c γ ∈ A * dA * } is infinite. Let Z β be the subshift d∈D O(z −∞ .dz +∞ ) ∪ O(z ∞ ).  ... 
doi:10.1016/j.jpaa.2008.08.009 fatcat:sineb3iksncmvnd7oa4fqu4rd4