30 citations · 132 across the 31 of their papers we have counts for
11 papers · 1 filter
Automaton semigroup constructions
Tara Brough, Alan J. Cain
The aim of this paper is to investigate whether the class of automaton semigroups is closed under certain semigroup constructions. We prove that the free product of two automaton s…
Rewriting systems and biautomatic structures for Chinese, hypoplactic, and sylvester monoids
Alan J. Cain, Robert D. Gray, António Malheiro
This paper studies complete rewriting systems and biautomaticity for three interesting classes of finite-rank homogeneous monoids: Chinese monoids, hypoplactic monoids, and sylvest…
For a few elements more: A survey of finite Rees index
Alan J. Cain, Victor Maltcev
This paper makes a comprehensive survey of results relating to finite Rees index for semigroups. In particular, we survey of the state of knowledge on whether various finiteness pr…
A simple non-bisimple congruence-free finitely presented monoid
Alan J. Cain, Victor Maltcev
We exhibit an example of a finitely presented monoid that is congruence-free and simple but not bisimple.
Hopfian and co-hopfian subsemigroups and extensions
Alan J. Cain, Victor Maltcev
This paper investigates the preservation of hopficity and co-hopficity on passing to finite-index subsemigroups and extensions. It was already known that hopficity is not preserved…
A countable family of finitely presented infinite congruence-free monoids
Alan J. Cain, Victor Maltcev, Abdullahi Umar
We prove that monoids are congruence-free for all . This provides a ne…