Related papers: Atomic Pseudo-Valuation Domains

Let $V$ be a valuation domain with quotient field $K$. Given a pseudo-convergent sequence $E$ in $K$, we study two constructions associating to $E$ a valuation domain of $K(X)$ lying over $V$, especially when $V$ has rank one. The first one…

Pseudo-variograms appear naturally in the context of multivariate Brown-Resnick processes, and are a useful tool for analysis and prediction of multivariate random fields. We give a necessary and sufficient criterion for a matrix-valued…

A preference domain is called a non-dictatorial domain if it allows the design of unanimous social choice functions (henceforth, rules) that are non-dictatorial and strategy-proof. We study a class of preference domains called…

A semidomain is an additive submonoid of an integral domain that is closed under multiplication and contains the identity element. Although atomicity and divisibility in integral domains have been systematically investigated for more than…

The notion of a pseudocycle is introduced by McDuff and Salamon (J-holomorphic curves and quantum cohomology, University Lecture Series, Vol. 6, AMS (1994)) to provide a framework for defining Gromov-Witten invariants and quantum…

In general, ring theory is focused on atomic rings, i.e. rings in which every element has some factorization into irreducible elements. In a recent paper of Boynton and Coykendall \cite{BC}, the two authors introduce two properties that are…

Let $V$ be a valuation domain with quotient field $K$. We show how to describe all extensions of $V$ to $K(X)$ when the $V$-adic completion $\widehat{K}$ is algebraically closed, generalizing a similar result obtained by Ostrowski in the…

In this article, we introduce pseudo-absolute values, which generalise usual absolute values. Roughly speaking, a pseudo-absolute value on a field $K$ is a map $|\cdot| : K \to [0,+\infty]$ satisfying axioms similar to those of usual…

We look at value functions of primes in simple Artinian rings and associate arithmetical pseudo-valuations to Dubrovin valuation rings which, in the Noetherian case, are $\mathbb{Z}$-valued. This allows a divisor theory for bounded Krull…

A subset $S$ of an integral domain $R$ is called a semidomain provided that the pairs $(S,+)$ and $(S, \cdot)$ are semigroups with identities. The study of factorizations in integral domains was initiated by Anderson, Anderson, and…

We study properties of pseudodifferential operators which arise in their use in boundary value problems. Smooth domains as well as intersections of smooth domains are considered.

Exceptional domains are domains on which there exists a positive harmonic function, zero on the boundary and such that the normal derivative on the boundary is constant. Recent results classify exceptional domains as belonging to either a…

In large-scale domain classification, an utterance can be handled by multiple domains with overlapped capabilities. However, only a limited number of ground-truth domains are provided for each training utterance in practice while knowing as…

For a polynomial ring over a commutative ring of positive characteristic, we define on the associated de Rham-Witt complex a set of functions, and show that they are pseudovaluations in the sense of Davis, Langer and Zink. To achieve it, we…

The main aim of this article is to study and develop valuation theory for Krasner hyperfields. In analogy with classical valuation theory for fields, we generalise the formalism of valuation rings to describe equivalence of valuations on…

In the early 1990's Andersen, Jantzen and Soergel introduced a category in order to give a combinatorial model for certain representations of quantum groups at a root of unity and simultaneously of Lie algebras of semisimple algebraic…

Since its introduction 25 years ago, the quantum weak value has gradually transitioned from a theoretical curiosity to a practical laboratory tool. While its utility is apparent in the recent explosion of weak value experiments, its…

In his unpublished preprint "Definable Valuations" Koenigsmann shows that every field that admits a t-henselian topology is either real closed or separably closed or admits a definable valuation inducing the t-henselian topology. To show…

Let $D$ be an integral domain. Then $D$ is an almost valuation (AV-)domain if for $a, b\in D\setminus \{0\}$ there exists a natural number $n$ with $a^{n}\mid b^{n}$ or $b^{n}\mid a^{n}$. AV-domains are closely related to valuation domains,…

Pseudoline arrangements are fundamental objects in discrete and computational geometry, and different works have tackled the problem of improving the known bounds on the number of simple arrangements of $n$ pseudolines over the past…