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A local structure theorem for stable, \(\mathcal {J}\)-simple semigroup biacts

  • Xavier MaryEmail author
RESEARCH ARTICLE
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Abstract

We describe a class of semigroup biacts that is analogous to the class of completely simple semigroups, and prove a structure theorem for those biacts that is analogous to the Rees–Sushkevitch Theorem. Precisely, we describe stable, \(\mathcal {J}\)-simple biacts in terms of wreath products, translations of completely simple semigroups, biacts over endomorphism monoids of free G-acts, tensor products and matrix biacts. Applications to coproducts and left acts are given.

Keywords

Semigroup acts Green’s relations Stability Wreath products Endomorphism monoid of free G-acts Completely simple semigroups Rees matrix semigroups 

Notes

Acknowledgements

This research has been conducted as part of the project Labex MME-DII (ANR11-LBX-0023-01). It also benefited from very fruitful conversations with members of the Department of Mathematics, University of York, while the present author was visiting the University.

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Modal’X, UPLUniv Paris NanterreNanterreFrance

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