1 citations · 2 across the 5 of their papers we have counts for
5 papers
A characterisation of semigroups with only countably many subdirect products with
Ashley Clayton, Catherine Reilly, Nik Ruškuc
Let be the additive (semi)group of integers. We prove that for a finite semigroup the direct product contains only countably many subdirect pr…
On the number of subdirect products involving semigroups of integers and natural numbers
Ashley Clayton, Katie Reilly, Nik Ruskuc
We extend a recent result that for the (additive) semigroup of positive integers , there are continuum many subdirect products of up to i…
On the number of countable subdirect powers of finite commutative semigroups
Ashley Clayton, Nik Ruskuc
In 1981/82, Hickin \& Plotkin and McKenzie both proved that a finite group has only countably many non-isomorphic subdirect powers if and only if it is abelian. In this paper, we p…
On finitary properties for fiber products of free semigroups and monoids
Ashley Clayton
We consider necessary and sufficient conditions for finite generation and finite presentability for fiber products of free semigroups and free monoids. We give a necessary and suff…
On the number of subsemigroups of direct products involving the free monogenic semigroup
Ashley Clayton, Nik Ruskuc
The direct product of two free monogenic semigroups contains uncountably many pairwise non-isomorphic subdirect products. Furthermore, the following ho…