Related papers: Universally free numerical semigroups
Given a finite, simple, vertex-weighted graph, we construct a graded associative (non-commutative) algebra, whose generators correspond to vertices and whose ideal of relations has generators that are graded commutators corresponding to…
We define a reflective numerical semigroup of genus $g$ as a numerical semigroup that has a certain reflective symmetry when viewed within $\mathbb{Z}$ as an array with $g$ columns. Equivalently, a reflective numerical semigroup has one gap…
Ideals generated by adjacent 2-minors are studied. First, the problem when such an ideal is a prime ideal as well as the problem when such an ideal possesses a quadratic Gr\"obner basis is solved. Second, we describe explicitly a primary…
A proper subsemigroup of a semigroup is maximal if it is not contained in any other proper subsemigroup. A maximal subsemigroup of a finite semigroup has one of a small number of forms, as described in a paper of Graham, Graham, and Rhodes.…
A smallest generating set of a semigroup is a generating set of the smallest cardinality. Similarly, an irredundant generating set $X$ is a generating set such that no proper subset of $X$ is also a generating set. A semigroup $S$ is…
We prove that the boundary dynamics of the (semi)group generated by the enriched dual transducer characterizes the algebraic property of being free for an automaton group. We specialize this result to the class of bireversible transducers…
We show that for every $N\ge 3$ the free unitary group $U^+_N$ is topologically generated by its classical counterpart $U_N$ and the lower-rank $U^+_{N-1}$. This allows for a uniform inductive proof that a number of finiteness properties,…
A semigroup is \emph{nilpotent} of degree 3 if it has a zero, every product of 3 elements equals the zero, and some product of 2 elements is non-zero. It is part of the folklore of semigroup theory that almost all finite semigroups are…
We examine two natural operations to create numerical semigroups. We say that a numerical semigroup $\mathcal{S}$ is $k$-normalescent if it is the projection of the set of integer points in a $k$-dimensional polyhedral cone, and we say that…
We give an explicit way of writing down a minimal set of generators for the canonical ideal of a non-degenerate curve, or of a more general smooth projective curve in a toric surface, in terms of its defining Laurent polynomial.
The algebra of quantum matrices of a given size supports a rational torus action by automorphisms. It follows from work of Letzter and the first named author that to understand the prime and primitive spectra of this algebra, the first step…
A new sufficient condition under which a semigroup admits no finite identity basis has been recently suggested in a joint paper by Karl Auinger, Yuzhu Chen, Xun Hu, Yanfeng Luo, and the author (see http://arxiv.org/abs/1405.0783). Here we…
We say that a nonselfadjoint operator algebra is partly free if it contains a free semigroup algebra. Motivation for such algebras occurs in the setting of what we call free semigroupoid algebras. These are the weak operator topology closed…
In this paper, we deal with the problem of uniqueness of minimal system of binomial generators of a semigroup ideal. Concretely, we give different necessary and/or sufficient conditions for uniqueness of such minimal system of generators.…
In combinatorial commutative algebra and algebraic statistics many toric ideals are constructed from graphs. Keeping the categorical structure of graphs in mind we give previous results a more functorial context and generalize them by…
In this paper, we study algorithmic problems for automaton semigroups and automaton groups related to freeness and finiteness. In the course of this study, we also exhibit some connections between the algebraic structure of automaton…
A numerical semigroup is an additive subsemigroup of the natural numbers that contains zero and has finite complement. A numerical semigroup is irreducible if it cannot be written as an intersection of numerical semigroups properly…
The notion of automatic selfadjointness of all ideals in a multiplicative semigroup of the bounded linear operators on a separable Hilbert space B(H) arose in a 2015 discussion with Heydar Radjavi who pointed out that B(H) and the finite…
For some numerical semigroup rings of small embedding dimension, namely those of embedding dimension 3, and symmetric or pseudosymmetric of embedding dimension 4, presentations has been determined in the literature. We extend these results…
We exhibit infinite, solvable, virtually abelian groups with a fixed number of generators, having arbitrarily large balls consisting of torsion elements. We also provide a sequence of 3-generator non-virtually nilpotent polycyclic groups of…