On residual finiteness of monoids, their Schützenberger groups and associated actions
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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.
Gray , R & Ruskuc , N 2014 , ' On residual finiteness of monoids, their Schützenberger groups and associated actions ' Journal of Algebra , vol 407 , pp. 21-45 . DOI: 10.1016/j.jalgebra.2014.02.025
Journal of Algebra
Copyright 2014, Elsevier. This is the author’s version of a work that was accepted for publication in Journal of Algebra. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Algebra, Vol 407, June 2014. DOI: http://dx.doi.org/10.1016/j.jalgebra.2014.02.025
RG was supported by an EPSRC Postdoctoral Fellowship EP/E043194/1 held at the University of St Andrews, Scotland.
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