Expansions of inverse semigroups

• Autores: Mark V. Lawson, Stuart W. Margolis, Benjamin Steinberg
• Localización: Journal of the Australian Mathematical Society, ISSN 1446-7887, Vol. 80, Nº 2, 2006, págs. 205-228
• Idioma: inglés
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• Resumen

  • We construct the freest idempotent-pure expansion of an inverse semigroup, generalizing an expansion of Margolis and Meakin for the group case. We also generalize the Birget-Rhodes prefix expansion to inverse semigroups with an application to partial actions of inverse semigroups. In the process of generalizing the latter expansion, we are led to a new class of idempotent-pure homomorphisms which we term F-morphisms. These play the same role in the theory of idempotent-pure homomorphisms that F-inverse monoids play in the theory of E-unitary inverse semigroups.