Related papers: W-Jaffard domains in pullbacks

The purpose of this paper is to explore more properties and representations of the W-weighted m-weak group (in short, W-m-WG) inverse. We first explore an interesting relation between two projectors with respect to the W-m-WG inverse. Then,…

Let v, w be infinite 0-1 sequences, and m a positive integer. We say that w is m-embeddable in v, if there exists an increasing sequence n_{i} of integers with n_{0}=0, such that 0< n_{i} - n_{i-1} < m, w(i) = v(n_i) for all i > 0. Let X…

We study the class of domains in which each w-ideal is divisorial, extending several properties of divisorial and totally divisorial domains to a much wider class of domains. In particular we consider PvMDs and Mori domains.

We prove the existence of nontrivial unbounded exceptional domains in the Euclidean space $\R^N$, $N\geq4$. These domains arise as perturbations of complements of straight cylinders in $\R^N$, and by definition they support a positive…

In 2022, Z.-W. Sun defined \begin{equation*} w_k^{(\alpha)}{(x)}=\sum_{j=1}^{k}w(k,j)^{\alpha}x^{j-1}, \end{equation*} where $k,\alpha$ are positive integers and $w(k,j)=\frac{1}{j}\binom{k-1}{j-1}\binom{k+j}{j-1}$. Let $(x)_{0}=1$ and…

We prove that the critical embedding $\mathrm{W}^{\mathbb{A},1}(B)\hookrightarrow \mathrm{W}^{k-1,\frac{n}{n-1}}$ holds if and only if the $k$-homogeneous, linear differential operator $\mathbb{A}$ on $\mathbb{R}^n$ from $\mathbb{R}^N$ to…

We study a W-algebra of central charge 2(k-1)/(k+2) with k a positive integer greater than 1

An integral domain is said to have the IDF property when every non-zero element of it has only a finite number of non-associate irreducible divisors. A counterexample has already been found showing that IDF property does not necessarily…

Given an integral domain $D$ with quotient field $\mathcal{Q}(D)$, the reciprocal complement of $D$ is the subring $R(D)$ of $\mathcal{Q}(D)$ whose elements are all the sums $\frac{1}{d_1}+\ldots+\frac{1}{d_n} $ for $d_1, \ldots, d_n$…

In this paper I consider all possible properties from commutative algebra for polynomial composites and monoid domains. The aim is full characterization of these structures. I start with the examination of group, ring, modules properties,…

This review paper deals with dimension theory of polynomial rings over certain families of pullbacks. While the literature is plentiful, this field is still developing and many contexts are yet to be explored. I will thus restrict the scope…

Let $\S $ be an arbitrary subset of $R^n$ where $R$ is a domain with the field of fractions $\K$. Denote the ring of polynomials in $n$ variables over $\K$ by $\K[\x].$ The ring of integer-valued polynomials over $\S,$ denoted by…

A commutative integral domain is primary if and only if it is one-dimensional and local. A domain is strongly primary if and only if it is local and each nonzero principal ideal contains a power of the maximal ideal. Hence one-dimensional…

A constructive procedure is proposed for formulation of linear differential equations invariant under global symmetry transformations forming a semi-simple Lie algebra f. Under certain conditions f-invariant systems of differential…

Fix a positive integer number $r$. A class of $r$-dim Lie conformal superalgebras named $r$-dim $i$-linear Lie conformal superalgebras are studied for $1\leq i \leq r$. We present an equivalent characterization of this class of Lie…

The reversal of a positive integer $A$ is the number obtained by reading $A$ backwards in its decimal representation. A pair $(A,B)$ of positive integers is said to be palindromic if the reversal of the product $A \times B$ is equal to the…

Fix a field $k$ of characteristic zero. If $a_1, ..., a_n$ ($n>2$) are positive integers, the integral domain $B = k[X_1, ..., X_n] / ( X_1^{a_1} + ... + X_n^{a_n} )$ is called a Pham-Brieskorn ring. It is conjectured that if $a_i > 1$ for…

In this article, we give a family of examples of algebras, showing that for every $n \geq 2$ and $m \geq 0$, there is an algebra displaying a path of n irreducible morphisms between indecomposable modules whose composite lies in the…

Assume $x,\ y,\ n$ are positive integers and $n$ is odd. In this note, we show that the class number of the imaginary quadratic field $\mathbb{Q}(\sqrt{x^{2}-y^{n}})$ is divisible by $n$ for fixed $x, n$ if $\gcd(2x,y)=1$ and $y>C$ where…

In this paper, we compare $(n,m)$-purities for different pairs of positive integers $(n,m)$. When $R$ is a commutative ring, these purities are not equivalent if $R$ doesn't satisfy the following property: there exists a positive integer…