THE FREE AMPLE MONOID-Reference-Cited by-同舟云学术

THE FREE AMPLE MONOID

Published:2009-06 Issue:04 Volume:19 Page:527-554
ISSN:0218-1967
Container-title:International Journal of Algebra and Computation
language:en
Short-container-title:Int. J. Algebra Comput.

Author:

FOUNTAIN JOHN¹,GOMES GRACINDA M. S.²³,GOULD VICTORIA¹

Affiliation:

1. Department of Mathematics, University of York, Heslington, York YO10 5DD, UK

2. Centro de Álgebra da Universidade de Lisboa, Av. Prof Gama Pinto, 2, 1649-003 Lisboa, Portugal

3. Departamento de Matemática, Faculdade de Ciências, Universidade de Lisboa, 1746–016 Lisboa, Portugal

Abstract

We show that the free weakly E-ample monoid on a set X is a full submonoid of the free inverse monoid FIM(X) on X. Consequently, it is ample, and so coincides with both the free weakly ample and the free ample monoid FAM(X) on X. We introduce the notion of a semidirect product Y*T of a monoid T acting doubly on a semilattice Y with identity. We argue that the free monoid X* acts doubly on the semilattice [Formula: see text] of idempotents of FIM(X) and that FAM(X) is embedded in [Formula: see text]. Finally we show that every weakly E-ample monoid has a proper ample cover.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218196709005214

Reference29 articles.

1. Connections between left adequate semigroups and γ-semigroups

2. A Course in Universal Algebra

3. Restriction categories I: categories of partial maps

4. A CLASS OF RIGHT PP MONOIDS

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