Related papers: On $v$-domains: a survey

The ring of periodic distributions on ${\mathbb{R}}^{\tt d}$ with usual addition and with convolution is considered. Via Fourier series expansions, this ring is isomorphic to the ring ${\mathcal{S}}'({\mathbb{Z}}^{\tt d})$ of all maps…

The study of graphs associated with of various algebraic structures is an emerging topic in algebraic graph theory. Recently, the concept of nonzero component graph of a finite dimensional vector space $\Gamma(\mathbb{V})$ was put forward…

Domain generalization (DG) aims to learn from multiple source domains a model that can generalize well on unseen target domains. Existing DG methods mainly learn the representations with invariant marginal distribution of the input…

We study a condition on intersections of localizations of a domain at maximal t-ideals. This extends and generalizes earlier work of Gilmer (1967), Gilmer-Heinzer (1968), Olberding (1998), and others for Prufer domains.

Let $R$ be a one-dimensional, local, Noetherian domain, $\R$ the integral closure of $R$ in its quotient field and $v(R)$ the value set defined by the usual valuation. The aim of the paper is to study the non-negative invariant…

This note investigates two long-standing conjectures on the Krull dimension of integer-valued polynomial rings and of polynomial rings, respectively, in the context of (locally) essential domains.

Let B be a commutative $\mathbb{Z}$-graded domain of characteristic zero. An element f of B is said to be cylindrical if it is nonzero, homogeneous of nonzero degree, and such that $B_{(f)}$ is a polynomial ring in one variable over a…

This paper surveys and develops links between polynomial invariants of finite groups, factorization theory of Krull domains, and product-one sequences over finite groups. The goal is to gain a better understanding of the multiplicative…

A new explicit construction of Cauchy-Fantappi\'e kernels is introduced for an arbitrary weakly pseudoconvex domain with smooth boundary. While not holomorphic in the parameter, the new kernel reflects the complex geometry and the Levi form…

It is well known that a domain without proper strongly divisorial ideals is completely integrally closed. In this paper we show that a domain without {\em prime} strongly divisorial ideals is not necessarily completely integrally closed,…

We establish properties of a new type of fractal which has partial self similarity at all scales. For any collection of iterated functions systems with an associated probability distribution and any positive integer V there is a…

The fractional integrals and fractional derivatives problem is tackled by using the operator approach. The definition domain E of operators is causal functions.Many properties of fractional integrals are given. Fractional derivatives…

Domain generalization (DG) aims to learn predictive models that can generalize to unseen domains. Most existing DG approaches focus on learning domain-invariant representations under the assumption of conditional distribution shift (i.e.,…

We observe that a finitely generated algebraic algebra R (over a field) is finite dimensional if and only if the associated graded ring grR is right noetherian, if and only if grR has right Krull dimension, if and only if grR satisfies a…

We study the method of finding conformal maps onto circle domains by approximating with finitely connected subdomains. Every domain $D \subset \hat{C}$ admits exhaustions, i.e., increasing sequences of finitely connected subdomains $D_j$…

We introduce and study the set of radical stable operations of an integral domain $D$. We show that their set is a complete lattice that is the join-completion of the set of spectral semistar operations, and we characterize when every…

This note intended to give a counterexample to a question related to the following theorem. Let D be a differential domain finitely generated over a differential field F with algebraically closed field of constants,C, of characteristic 0.…

Let R be a ring and X = SH(R)-{0} be the set of all non-zero strongly hollow ideals (briefly, sh-ideals) of R. We first study the concept SH-topology and investigate some of the basic properties of a topological space with this topology. It…

Let $D$ be an integral domain with quotient field $K$ and $\Omega$ a finite subset of $D$. McQuillan proved that the ring ${\rm Int}(\Omega,D)$ of polynomials in $K[X]$ which are integer-valued over $\Omega$, that is, $f\in K[X]$ such that…

Local Noetherian domains arising as local rings of points of varieties or in the context of algebraic number theory are analytically unramified, meaning their completions have no nontrivial nilpotent elements. However, looking elsewhere,…