Semigroups of finite matrices.
Semigroups of mappings on graphs.
Semigroups of order preserving mappings on a finite chain: a new class of divisors.
Semigroups of order-decreasing transformations: the isomorphism theorem.
Semigroups of order-preserving partial endomorphisms on trees, I
Semigroups of transformations restricted by an equivalence
Suppose σ is an equivalence on a set X and let E(X, σ) denote the semigroup (under composition) of all α: X → X such that σ ⊆ α ∘ α −1. Here we characterise Green’s relations and ideals in E(X, σ). This is analogous to recent work by Sullivan on K(V, W), the semigroup (under composition) of all linear transformations β of a vector space V such that W ⊆ ker β, where W is a fixed subspace of V.
Semigroups whose regular ... -classes form well-ordered chains.
Semigroups whose regular J-classes form finite lattices.
Semigroups with exactly three regular ...-classes.
Semigroups with only finitely many regular ... -classes.
Simultaneous representations by metric spaces
Some constructions related to Rees matrix rings.
Some decision problems on integer matrices
Given a finite set of matrices with integer entries, consider the question of determining whether the semigroup they generated 1) is free; 2) contains the identity matrix; 3) contains the null matrix or 4) is a group. Even for matrices of dimension , questions 1) and 3) are undecidable. For dimension , they are still open as far as we know. Here we prove that problems 2) and 4) are decidable by proving more generally that it is recursively decidable whether or not a given non singular matrix belongs...
Some decision problems on integer matrices
Given a finite set of matrices with integer entries, consider the question of determining whether the semigroup they generated 1) is free; 2) contains the identity matrix; 3) contains the null matrix or 4) is a group. Even for matrices of dimension 3, questions 1) and 3) are undecidable. For dimension 2, they are still open as far as we know. Here we prove that problems 2) and 4) are decidable by proving more generally that it is recursively decidable whether or not a given non singular matrix belongs...
Some monothetic subsemigroups of S(R).
Some observations on left absolutely flat monoids.
Some open problems and directions for further research in semigroups of continuous selfmaps
Some remarks on finite full transformation semigroups.
Some remarks on T-semigroups
Some results on generalized inverse semigroups.