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Acta Mathematica Hungarica

, Volume 141, Issue 1–2, pp 36–57 | Cite as

Proper restriction semigroups – semidirect products and W-products

  • Victoria Gould
  • Mária B. SzendreiEmail author
Article

Abstract

Fountain and Gomes [4] have shown that any proper left ample semigroup embeds into a so-called W-product, which is a subsemigroup of a reverse semidirect product \({T\ltimes {\mathcal {Y}}}\) of a semilattice \({\mathcal {Y}}\) by a monoid T, where the action of T on \({\mathcal {Y}}\) is injective with images of the action being order ideals of \({\mathcal {Y}}\). Proper left ample semigroups are proper left restriction, the latter forming a much wider class. The aim of this paper is to give necessary and sufficient conditions on a proper left restriction semigroup such that it embeds into a W-product. We also examine the complex relationship between W-products and semidirect products of the form \({{\mathcal {Y}}\rtimes T}\).

Key words and phrases

(left) restriction semigroup semidirect product W-product 

Mathematics Subject Classification

20M10 

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2013

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of YorkHeslington, YorkUK
  2. 2.Bolyai InstituteUniversity of SzegedSzegedHungary

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