2010
DOI: 10.1007/s00233-010-9236-z
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Semidirect product with an order-computable pseudovariety and tameness

Abstract: Abstract. The semidirect product of pseudovarieties of semigroups with an order-computable pseudovariety is investigated. The essential tool is the natural representation of the corresponding relatively free profinite semigroups and how it transforms implicit signatures. Several results concerning the behavior of the operation with respect to various kinds of tameness properties are obtained as applications.

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Cited by 5 publications
(9 citation statements)
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“…Following a concept introduced in [5], for a given implicit signature σ, we define a (σ, D k )expressible signature as an implicit signature σ ′ such that i) β ′ A (Ω σ ′ A S) ⊆ Ω σ B k S for any alphabet A; ii) there is an algorithm that computes, from a given alphabet A and a given σ…”
Section: Implicit Signaturesmentioning
confidence: 99%
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“…Following a concept introduced in [5], for a given implicit signature σ, we define a (σ, D k )expressible signature as an implicit signature σ ′ such that i) β ′ A (Ω σ ′ A S) ⊆ Ω σ B k S for any alphabet A; ii) there is an algorithm that computes, from a given alphabet A and a given σ…”
Section: Implicit Signaturesmentioning
confidence: 99%
“…As an application, we deduce that V * D is pointlike κ-reducible when V is pointlike κ-reducible, where κ denotes the canonical signature consisting of the multiplication and the (ω − 1)-power. Our starting point is the paper [5] of the first and third authors in collaboration with Almeida, where a similar study was performed for semidirect products with an order-computable pseudovariety and various kinds of reducibility properties. For each positive integer k, the pseudovariety D k defined by the identity yx 1 · · · x k = x 1 · · · x k is order-computable, and k D k = D. We use results of [5] concerning the pseudovarieties D k to derive our results relative to D and the pointlike reducibility property.…”
Section: Introductionmentioning
confidence: 99%
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“…There are various results using tameness of pseudovarieties to establish the decidability of pseudovarieties obtained by application of the operations of semidirect product, Mal'cev product and join [5,4,6].…”
Section: Introductionmentioning
confidence: 99%
“…There are various results using tameness of pseudovarieties to establish the decidability of pseudovarieties obtained by application of the operations of semidirect product, Mal'cev product and join [6,4,7].…”
Section: Introductionmentioning
confidence: 99%