Related papers: W-Jaffard domains in pullbacks
In this paper we consider the graded going-down property of graded integral domains in pullbacks. It then enables us to give original examples of these domains.
In this note we show that an integral domain $D$ of finite $w$-dimension is a quasi-Pr\"{u}fer domain if and only if each overring of $D$ is a $w$-Jaffard domain. Similar characterizations of quasi-Pr\"{u}fer domains are given by replacing…
An outstanding open question, which has attracted renewed attention following the pioneering work of Huang--Li--Treuer, is whether, for a given positive integer $m$, there exists a complex manifold whose Bergman metric is locally isometric…
We introduce and study a new class of integral domains which we call irreducible divisor pair domains (IDPDs). In particular, we show how IDPDs fit in with other classes of integral domains defined in terms of factorization conditions. For…
In this paper, we introduce the notion of a $w$-Hilbert domain and investigate its basic properties. More precisely, we explore its relationship with Hilbert domains, strong Mori domains, and UMT domains by providing various examples using…
In a previous paper, the author together with prof. dr. Finston constructed a class of UFDs A_{n,m} where n,m\in \N^*. These rings are all stably equivalent (A_{n,m}[T]\cong A_{p,q}[T] for all n,m,p,q) but are only isomorphic themselves if…
The humble $\dagger$ ("dagger") is used to denote two different operations in category theory: Taking the adjoint of a morphism (in dagger categories) and finding the least fixed point of a functional (in categories enriched in domains).…
Let A be a hereditary algebra over an algebraically closed field. We prove that an exact fundamental domain for the m-cluster category of A is the m-left part of the m-replicated algebra $A^{(m)}$ of A. Moreover, we obtain a one-to-one…
Recently it has been discovered that the W-algebras (orbifold of) WD_n can be defined even for negative integers n by an analytic continuation of their coupling constants. In this letter we shall argue that also the algebras WA_{-n-1} can…
Let $\{ R_n, {\mathfrak m}_n \}_{n \ge 0}$ be an infinite sequence of regular local rings with $R_{n+1}$ birationally dominating $R_n$ and ${\mathfrak m}_nR_{n+1}$ a principal ideal of $R_{n+1}$ for each $n$. We examine properties of the…
We give a simple and more elementary proof that the notions of Domain of Holomorphy and Weak Domain of Holomorphy are equivalent. This proof is based on a combination of Baire's Category Theorem and Montel's Theorem. We also obtain…
To study the question of whether every two-dimensional Pr\"ufer domain possesses the stacked bases property, we consider the particular case of the Pr\"ufer domains formed by integer-valued polynomials. The description of the spectrum of…
It is a well-known and easily established fact that every Euclidean domain is also a principal ideal domain. However, the converse statement is not true, and this is usually shown by exhibiting as a counterexample the ring of algebraic…
For a property $\mathcal{X}$ of integral domains, an integral domain $D$ is said to be a {\it locally $\mathcal{X}$-domain} if $D_P$ has the property $\mathcal{X}$ for every prime ideal $P$ of $D$. In this paper, we study the transfer of…
The notion of an Egyptian domain (where the analogue of Egyptian fractions works appropriately), first explored by Guerrieri-Loper-Oman, is extended to the more general notions of generically and locally Egyptian domains. Results from the…
We study those integral domains in which every proper ideal can be written as an invertible ideal multiplied by a nonempty product of proper radical ideals.
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…
A result by C. C.-A. Cheng, J. H. Mckay and S. S.-S. Wang says the following: Suppose the Jacobian of $A$ and $B$ is invertible in $\mathbb{C}[x,y]$ and the Jacobian of $A$ and $w$ is zero for $A,B,w \in \mathbb{C}[x,y]$. Then $w \in…
Given a right R-module M and any short exact sequence of right R-modules \[ 0 \to A \to B \to C \to 0, \] it is well known that if both A and C belong to the subinjectivity domain $\mathfrak{\underline{In}^{-1}}(M)$ (resp., the…
In this paper we prove that for any infinite word W whose set of factors is closed under reversal, the following conditions are equivalent: (I) all complete returns to palindromes are palindromes; (II) P(n) + P(n+1) = C(n+1) - C(n) + 2 for…