Related papers: Indispensable binomials in semigroup ideals
We study ideal-theoretic conditions for a monomial ideal to be Golod. For ideals in a polynomial ring in three variables, our criteria give a complete characterization. Over such rings, we show that the product of two monomial ideals is…
The problem of finding and characterizing minimal sets of dequantizers and quantizers applied in the mapping of operators onto functions is considered, for finite-dimensional quantum systems. The general properties of such sets are…
In our paper "Essential normality, essential norms and hyperrigidity" we claimed that the restriction of the identity representation of a certain operator system (constructed from a polynomial ideal) has the unique extension property,…
We first establish a sufficient condition for an additively idempotent semiring to be nonfinitely based. As applications, we exhibit several examples of additively idempotent semirings satisfying this condition, including a $4$-element…
We investigate whether the group algebra of a finite group over a localisation of the integers is semiperfect. The main result is a necessary and sufficient arithmetic criterion in the ordinary case. In the modular case, we propose a…
This paper studies a class of binomial ideals associated to graphs with finite vertex sets. They generalize the binomial edge ideals, and they arise in the study of conditional independence ideals. A Gr\"obner basis can be computed by…
A necessary condition for uniqueness of factorizations of elements of a finite group $G$ with factors belonging to a union of some conjugacy classes of $G$ is given. This condition is sufficient if the number of factors belonging to each…
This article introduces patterns of ideals of numerical semigroups, thereby unifying previous definitions of patterns of numerical semigroups. Several results of general interest are proved. More precisely, this article presents results on…
In this paper we completely characterize lattice ideals that are complete intersections or equivalently complete intersections finitely generated semigroups of $\bz^n\oplus T$ with no invertible elements, where $T$ is a finite abelian…
The quantum marginal problem is concerned with characterizing which collections of quantum states on different subsystems are compatible in the sense that they are the marginals of some multipartite quantum state. Presented here is a…
We provide algorithms for performing computations in generalized numerical semigroups, that is, submonoids of $\mathbb{N}^{d}$ with finite complement in $\mathbb{N}^{d}$. These semigroups are affine semigroups, which in particular implies…
We study infinitesimal generators of one-parameter semigroups in the unit disk $\mathbb D$ having prescribed boundary regular fixed points. Using an explicit representation of such infinitesimal generators in combination with Krein-Milman…
Motivated by intuitive properties of physical quantities, the notion of a non-anomalous semigroup is formulated. These are totally ordered semigroups where there are no `infinitesimally close' elements. The real numbers are then defined as…
We exhibit a 6-element semigroup that has no finite identity basis but nevertheless generates a variety whose finite membership problem admits a polynomial algorithm.
Necessary and sufficient conditions for finite semihypergroups to be built from groups of the same order are established
We give simple necessary and sufficient conditions for the inclusion-exclusion identity to hold for an infinite countable number of sets. In terms of a random variable, whose range are nonnegative integers, this condition is equivalent to…
Ideals in BIT speciale varieties are characterized. In particular, it is proved that, for any finitary BIT speciale variety, there is a finite set of ideal terms determining ideals. Several ideal term sets of this kind are given. For the…
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…
This paper presents a novel approach to constructing finite generating sets for infinitely generated ideals. By integrating algebraic and computational techniques, we provide a method to identify finite generators, demonstrated through…
We show that the number of elements generating a squarefree monomial ideal up to radical can always be bounded above in terms of the number of its minimal monomial generators and the maximal height of its minimal primes.