On residual finiteness of monoids, their Schützenberger groups and associated actions
Abstract
In this paper we discuss connections between the following properties: (RFM) residual finiteness of a monoid M ; (RFSG) residual finiteness of Schützenberger groups of M ; and (RFRL) residual finiteness of the natural actions of M on its Green's R- and L-classes. The general question is whether (RFM) implies (RFSG) and/or (RFRL), and vice versa. We consider these questions in all the possible combinations of the following situations: M is an arbitrary monoid; M is an arbitrary regular monoid; every J-class of M has finitely many R- and L-classes; M has finitely many left and right ideals. In each case we obtain complete answers, which are summarised in a table.
Citation
Gray , R & Ruskuc , N 2014 , ' On residual finiteness of monoids, their Schützenberger groups and associated actions ' , Journal of Algebra , vol. 407 , pp. 21-45 . https://doi.org/10.1016/j.jalgebra.2014.02.025
Publication
Journal of Algebra
Status
Peer reviewed
ISSN
0021-8693Type
Journal article
Description
RG was supported by an EPSRC Postdoctoral Fellowship EP/E043194/1 held at the University of St Andrews, Scotland.Collections
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