Related papers: Tight closure and continuous closure

For any pseudoconvex Runge domain $\Omega\subset\mathbb{C}^2$ we prove that every closed discrete subset in $\Omega$ is contained in a properly embedded complex curve in $\Omega$ with any prescribed topology (possibly infinite).

In order to better understand the structure of closed collections of reversible gates, we investigate the lattice of closed sets and the maximal members of this lattice. In this note, we find the maximal closed sets over a finite alphabet.…

We give short, closure-theoretic proofs for uniform bounds on the growth of symbolic powers of ideals in regular rings. The author recently proved these bounds in mixed characteristic using various versions of perfectoid/big Cohen-Macaulay…

We consider varieties generated by finite closure algebras whose canonical relations have two levels, and whose restriction to a level is an "extremal" relation, i.e. the identity or the universal relation. The corresponding logics have…

Let $\mathbf{k}$ be a field which is either finite or algebraically closed and let $R = \mathbf{k}[x_1,\ldots,x_n].$ We prove that any $g_1,\ldots,g_s\in R$ homogeneous of positive degrees $\le d$ are contained in an ideal generated by an…

We prove that the category of countable Tate modules over an arbitrary discrete ring embeds fully faithfully into that of condensed modules. If the base ring is of finite type, we characterize the essential image as generated by the free…

A new proof of the classification for tensor ideal thick subcategories of the bounded derived category, and the stable category, of modular representations of a finite group is obtained. The arguments apply more generally to yield a…

Let A be a Noetherian ring and B be a finitely generated A-algebra. Denote by A' the integral closure of A in B. We give necessary and sufficient conditions for prime ideals to be in Ass_{A}(B/A') and Ass_{A'}(B/A') generalizing and…

We provide a complete characterization of closed sets with empty interior and positive reach in $\mathbb{R}^2$. As a consequence, we characterize open bounded domains in $\mathbb{R}^2$ whose high ridge and cut locus agree, and hence $C^1$…

Internal categories feature notions of limit and completeness, as originally proposed in the context of the effective topos. This paper sets out the theory of internal completeness in a general context, spelling out the details of the…

The aim of this article is to give a rigorous geometric interpretation of the completion of a ring with respect to an ideal. To this end, we define the infinitesimal neighbourhood of an immersion of formal schemes as the largest possible…

It is established a continuous boundary extension of some class of mappings. Under some additional conditions, we have established that this extension is light in the closure of the definition domain. Under some stronger conditions, we also…

Following "An infinite dimensional Schur-Horn theorem and majorization theory", Journal of Functional Analysis 259 (2010) 3115-3162, this paper further studies majorization for infinite sequences. It extends to the infinite case classical…

In this paper, we study the differential power operation on ideals. We begin with a focus on monomial ideals in characteristic 0 and find a class of ideals whose differential powers are eventually principal. We also study the containment…

The Qth-power algorithm for computing structured global presentations of integral closures of affine domains over finite fields is modified to compute structured presentations of integral closures of ideals in affine domains over finite…

Let $k$ be a field, let $A$ and $B$ be polynomial rings over $k$, and let $S= A \otimes_k B$. Let $I \subseteq A$ and $J \subseteq B$ be monomial ideals. We establish a binomial expansion for rational powers of $I+J \subseteq S$ in terms of…

This paper investigates t-reductions of ideals in pullback constructions. Section 2 examines the correlation between the notions of reduction and t-reduction in pseudo-valuation domains. Section 3 solves an open problem on whether the…

We obtain estimates of the modulus of continuity for the real part of the Cauchy-type integral in the closure of domain bounded by an Ahlfors-regular integration curve. These estimates are more exact than the well-known Zygmund estimate for…

We give a type system in which the universe of types is closed by reflection into it of the logical relation defined externally by induction on the structure of types. This contribution is placed in the context of the search for a natural,…

We define the notion of rational closure in the context of Description Logics extended with a tipicality operator. We start from ALC+T, an extension of ALC with a typicality operator T: intuitively allowing to express concepts of the form…