Related papers: Certain observations on selection principles relat…

We focus on the structure of a homogeneous Gorenstein ideal $I$ of codimension three in a standard polynomial ring $R=\kk[x_1,\ldots,x_n]$ over a field $\kk$, assuming that $I$ is generated in a fixed degree $d$. For such an ideal $I$ this…

We present a close relationship between matching number, covering numbers and their fractional versions in combinatorial optimization and ordinary powers, integral closures of powers, and symbolic powers of monomial ideals. This…

Let $R=\mathbb{K}[X_1, \ldots , X_n ]$ be a polynomial ring over a field $\mathbb{K}$. We introduce an endomorphism $\mathcal{F}^{[m]}: R \rightarrow R $ and denote the image of an ideal $I$ of $R$ via this endomorphism as $I^{[m]}$ and…

We show some basic results on the characterization of quasi-Polish spaces in terms of spaces of ideals, with an emphasis on the connections with computable topology.

This article aims to explore the bridge between the algebraic structure of a linear code and the complete decoding process. To this end, we associate a specific binomial ideal $I_+(\mathcal C)$ to an arbitrary linear code. The binomials…

We describe the second homotopy group of any CW-complex $K$ by analyzing the universal cover of a locally finite model of $K$ using the notion of $G$-coloring of a partially ordered set. As applications we prove a generalization of the…

Our work was motivated by a recent study on birth defects of infants born to pregnant women exposed to a certain medication for treating chronic diseases. Outcomes such as birth defects are rare events in the general population, which often…

We define and study Hodge ideals associated to a coherent ideal sheaf J on a smooth complex variety, via algebraic constructions based on the already existing concept of Hodge ideals associated to Q-divisors. We also define the generic…

Sufficient conditions for an ideal $\mathcal I$ in $R\Mod$ to be covering are proved. This allows to obtain an alternative proof of the existence of phantom covers of modules. Our approach is inspired by an extension of the standard…

We give a general method to reduce Hurewicz-type selection hypotheses into standard ones. The method covers the known results of this kind and gives some new ones. Building on that, we show how to derive Ramsey theoretic characterizations…

Let $S = \mathsf{k}[x_1, \ldots, x_n]$, $I$ be an ideal of $S$, and $\bar{I}$ denote its integral closure. A conjecture of K\"{u}ronya and Pintye states that for any homogeneous ideal $I$ of $S$, the inequality $\operatorname{reg}(\bar{I})…

We describe the Chow homology and cohomology of toric variety bundles, with no restrictions on the singularities of the fibre. We present the ordinary and equivariant homologies as modules over the cohomology of the base, identify the…

In this paper we continue the development of a new technique for computing elimination ideals by substitution which has been called $Z$-separating re-embeddings. Given an ideal $I$ in the polynomial ring $K[x_1,\dots,x_n]$ over a field $K$,…

We prove that a monomial ideal $I$ generated in a single degree, is polymatroidal if and only if it has linear quotients with respect to the lexicographical ordering of the minimal generators induced by every ordering of variables. We also…

We introduce a "workable" notion of degree for non-homogeneous polynomial ideals and formulate and prove ideal theoretic B\'ezout Inequalities for the sum of two ideals in terms of this notion of degree and the degree of generators. We…

We define combinatorial representations of finite skew braces and use this idea to produce a database of skew braces of small size. This database is then used to explore different concepts of the theory of skew braces such as ideals, series…

We want to give a construction as simple as possible of a Borel subset of a product of two Polish spaces. This introduces the notion of potential Wadge class. Among other things, we study the non-potentially closed sets, by proving…

Motivated by analogies with basic density theorems in analytic number theory, we introduce a notion (and variations) of the homological density of one space in another. We use Weil's number field/ function field analogy to predict…

In this paper we study ideals generated by quite general sets of 2-minors of an $m \times n$-matrix of indeterminates. The sets of 2-minors are defined by collections of cells and include 2-sided ladders. For convex collections of cells it…

Measurability with respect to ideals is tightly connected with absoluteness principles for certain forcing notions. We study a uniformization principle that postulates the existence of a uniformizing function on a large set, relative to a…