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On the equation V∗G=EV
2002
Journal of Pure and Applied Algebra
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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
2013
International journal of algebra and computation
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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
2002
International journal of algebra and computation
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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
2009
Journal of Pure and Applied Algebra
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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