On residual finiteness of monoids, their Schützenberger groups and associated actions

  title={On residual finiteness of monoids, their Sch{\"u}tzenberger groups and associated actions},
  author={Robert D. Gray and Nik Ru{\vs}kuc},
  journal={Journal of Algebra},

Figures and Tables from this paper

Taking residual finiteness as a starting point, we consider three related finiteness properties: weak subsemigroup separability, strong subsemigroup separability and complete separability. We
Rewriting systems and biautomatic structures for Chinese, hypoplactic, and sylvester monoids
This paper studies complete rewriting systems and biautomaticity for three interesting classes of finite-rank homogeneous monoids: Chinese monoid, hypoplactic monoids, and sylvester monoids; the monoid algebras corresponding to monoids of these classes are automaton algeBRas in the sense of Ufnarovskij.
Separability conditions in acts over monoids
. We discuss residual finiteness and several related separability conditions for the class of monoid acts, namely weak subact separability, strong subact separability and complete separability. For
Some Finiteness Conditions for Strong Semilattice of Semigroups
Let be a strong semilattice of semigroups such that is finite and each be a family of disjoint semigroups. In this article some finiteness conditions which are periodicity, local finiteness and
A classification of disjoint unions of two or three copies of the free monogenic semigroup
We prove that, up to isomorphism and anti-isomorphism, there are only two types of semigroups which are the union of two copies of the free monogenic semigroup. Similarly, there are only nine types
On disjoint unions of finitely many copies of the free monogenic semigroup
Every semigroup which is a finite disjoint union of copies of the free monogenic semigroup (natural numbers under addition) is finitely presented and residually finite.


On finite presentability of monoids and their Schützenberger groups
In [24, Theorem 4.1] it was proved that a regular monoid S with finitely many left and right ideals is finitely presented if and only if all its maximal subgroups are finitely presented. Recall that
Note on residually finite rings
This paper is on the subject of residually finite (= RF) modules and rings introduced by Varadarajan [93] and [98/99]. Specifically there are several theorems that simplify proofs and generalize some
Rings with all modules residually finite
AbstractDefine a ringA to be RRF (resp. LRF) if every right (resp. left) A-module is residually finite. Refer to A as an RF ring if it is simultaneously RRF and LRF. The present paper is devoted to
Green index and finiteness conditions for semigroups
On residual finiteness of direct products of algebraic systems
It is well known that if two algebraic structures A and B are residually finite then so is their direct product. Here we discuss the converse of this statement. It is of course true if A and B
The algebraic theory of semigroups
This book, along with volume I, which appeared previously, presents a survey of the structure and representation theory of semi groups. Volume II goes more deeply than was possible in volume I into
Residual finiteness of color Lie superalgebras
A (color) Lie superalgebra L over a field K of characteristic ¬= 2, 3 is called residually finite if any of its nonzero elements remains nonzero in a finite-dimensional homomorphic image of L. In
Some Connections between Residual Finiteness, Finite Embeddability and the Word Problem
Finite embeddability. An algebra A is residually finite if for any x # y in A, there is a homomorphism a of A onto a finite algebra such that xct # yu. For the notion of an incomplete or partial
Syntactic and Rees Indices of Subsemigroups
Abstract We define two different notions of index for subsemigroups of semigroups: the (right) syntactic index and the Rees index. We investigate the relationships between them and with the group
Residual finiteness of free products of combinatorial strict inverse semigroups
It is shown that the free product of two residually finite combinatorial strict inverse semigroups in general is not residually finite. In contrast, the free product of a residually finite