5 citations · 6 across the 10 of their papers we have counts for
13 papers
Howson property and finitely generated intersection problem for monogenic inverse semigroups
Jung Won Cho, Craig Miller, Nik Ruškuc
An algebraic structure is said to have the Howson property if the intersection of any two finitely generated subalgebras is finitely generated. We explore the Howson property in th…
On minimal conditions in semigroups and biacts
Craig Miller
We systematically study the minimal conditions on -, - and -classes, denoted by , and , as well as the related notions of lef…
The ascending chain condition on principal right ideals for semigroup constructions
Craig Miller
We call a semigroup -noetherian if it satisfies the ascending chain condition on principal right ideals, or, equivalently, the ascending chain condition on $\mathcal{R…
Ascending chain conditions on right ideals of semigroups
Craig Miller
We call a semigroup right noetherian if it satisfies the ascending chain condition on right ideals, and we say that satisfies ACCPR if it satisfies the ascending chain cond…
On minimal ideals in pseudo-finite semigroups
Victoria Gould, Craig Miller, Thomas Quinn-Gregson +1
A semigroup is said to be right pseudo-finite if the universal right congruence can be generated by a finite set , and there is a bound on the length of d…
The -height of semigroups and their bi-ideals
Craig Miller
The -height of a semigroup is the height of the poset of -classes of i.e. the supremum of the lengths of chains of -classes. Given a…
Separability conditions in acts over monoids
Craig Miller
We discuss residual finiteness and several related separability conditions for the class of monoid acts, namely weak subact separability, strong subact separability and complete se…
Semigroups whose right ideals are finitely generated
Craig Miller
We call a semigroup weakly right noetherian if every right ideal of is finitely generated; equivalently, satisfies the ascending chain condition on right ideals. We pro…
On separability finiteness conditions in semigroups
Craig Miller, Gerard O'Reilly, Martyn Quick +1
Taking residual finiteness as a starting point, we consider three related finiteness properties: weak subsemigroup separability, strong subsemigroup separability and complete separ…
Semigroups for which every right congruence of finite index is finitely generated
Craig Miller
We call a semigroup f-noetherian if every right congruence of finite index on is finitely generated. We prove that every finitely generated semigroup is f-noetherian, and i…
Right noetherian semigroups
Craig Miller, Nik Ruskuc
A semigroup is right noetherian if every right congruence on is finitely generated. In this paper we present some fundamental properties of right noetherian semigroups, dis…
Generators and presentations for direct and wreath products of monoid acts
Craig Miller
We investigate the preservation of the properties of being finitely generated and finitely presented under both direct and wreath products of monoid acts. A monoid is said to p…
An introduction to presentations of monoid acts: quotients and subacts
Craig Miller, Nik Ruskuc
The purpose of this paper is to introduce the theory of presentations of monoids acts. We aim to construct `nice' general presentations for various act constructions pertaining to…