35 citations · 42 across the 18 of their papers we have counts for
20 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…
Maximal subgroups of free projection- and idempotent-generated semigroups with applications to partition monoids
James East, Robert D. Gray, P. A. Azeef Muhammed +1
This paper investigates the maximal subgroups of a free projection-generated regular -semigroup over a projection algebra , and their relationship to the maximal subg…
Twisted products of monoids
James East, Robert D. Gray, P. A. Azeef Muhammed +1
A twisting of a monoid is a map satisfying the identity . Together with an additive commutative monoid , and…
Semigroup Congruences and Subsemigroups of the Direct Square
Callum Barber, Nik Ruškuc
We investigate semigroups which have the property that every subsemigroup of which contains the diagonal is necessarily a congruence on $S…
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…
Filtered Boolean powers of finite simple non-abelian Mal'cev algebras
Peter Mayr, Nik Ruškuc
Let be a finite simple non-abelian Mal'cev algebra (e.g. a group, loop, ring). We investigate the Boolean power of by the countable atomless…
On Finite Presentability of Subsemigroups of the Monogenic Free Inverse Semigroup
Yung Won Cho, Nik Ruskuc
The monogenic free inverse semigroup is not finitely presented as a semigroup due to the classic result by Schein (1975). We extend this result and prove that a finitely gen…
Graph products of residually finite monoids are residually finite
Jung Won Cho, Victoria Gould, Nik Ruškuc +1
We show that any graph product of residually finite monoids is residually finite. As a special case we obtain that any free product of residually finite monoids is residually finit…
Congruences of maximum regular subsemigroups of variants of finite full transformation semigroups
Igor Dolinka, James East, Nik Ruškuc
Let be the full transformation monoid over a finite set , and fix some of rank . The variant has underlying set , and operation .…
Generators and presentations of inverse subsemigroups of the monogenic free inverse semigroup
Jung Won Cho, Nik Ruskuc
It was proved by Oliveira and Silva (2005) that every finitely generated inverse subsemigroup of the monogenic free inverse semigroup is finitely presented. The present pape…
Coherency properties for monoids of transformations and partitions
Matthew Brookes, Victoria Gould, Nik Ruskuc
A monoid is right coherent if every finitely generated subact of every finitely presented right -act itself has a finite presentation; it is weakly right coherent if every f…
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…
Heights of one- and two-sided congruence lattices of semigroups
M. Brookes, J. East, C. Miller +2
The height of a poset is the supremum of the cardinalities of chains in . The exact formula for the height of the subgroup lattice of the symmetric group is…
On the diameter of semigroups of transformations and partitions
James East, Victoria Gould, Craig Miller +2
For a semigroup whose universal right congruence is finitely generated (or, equivalently, a semigroup satisfying the homological finiteness property of being type right-)…
Decidability of well quasi-order and atomicity for equivalence relations under embedding orderings
V. Ironmonger, N. Ruskuc
We consider the posets of equivalence relations on finite sets under the standard embedding ordering and under the consecutive embedding ordering. In the latter case, the relations…
On the number of countable subdirect powers of unary algebras
Nik Ruskuc, Bill de Witt
A finite unary algebra has only countably many countable subdirect powers if and only if every operation is either a permutation or a constant mapping.
On hopfian cofinite subsemigroups
Victor Maltcev, N. Ruskuc
If a finitely generated semigroup S has a hopfian (meaning: every surjective endomorphism is an automorphism) cofinite subsemigroup T then S is hopfian too. This no longer holds if…
Ideals and finiteness conditions for subsemigroups
R. Gray, V. Maltcev, J. D. Mitchell +1
In this paper we consider a number of finiteness conditions for semigroups related to their ideal structure, and ask whether such conditions are preserved by sub- or supersemigroup…
Maximal subgroups of free idempotent generated semigroups over the full transformation monoid
Robert Gray, Nik Ruskuc
Let T_n be the full transformation semigroup of all mappings from the set {1,...,n} to itself under composition. Let E = E(T_n) denote the set of idempotents of T_n and let e be an…
On Maximal Subgroups of Free Idempotent Generated Semigroups
Robert Gray, Nik Ruskuc
We prove the following results: (1) Every group is a maximal subgroup of some free idempotent generated semigroup. (2) Every finitely presented group is a maximal subgroup of some…