Related papers: Some normal monomial ideals
The main goal of the paper is the discussion of a deeper interaction between matrix theory over polynomial rings over a field and typical methods of commutative algebra and related algebraic geometry. This is intended in the sense of…
In this paper, we study the classes of rings in which every proper (regular) ideal can be factored as an invertible ideal times a nonempty product of proper radical ideals. More precisely, we investigate the stability of these properties…
This study investigates the structure of Arf rings. From the perspective of ring extensions, a decomposition of integrally closed ideals is given. Using this, we present a kind of their prime ideal decomposition in Arf rings, and determine…
In this paper we study injective modules over universal enveloping algebras of finite-dimensional Lie algebras over fields of arbitrary characteristic. Most of our results are dealing with fields of prime characteristic but we also…
This article investigates various notions of primeness for one-sided ideals in noncommutative rings, with a focus on principal ideal domains.
The aim of this paper is to characterize simplicial complexes which have standard graded vertex cover algebras. This property has several nice consequences for the squarefree monomial ideals defining these algebras. It turns out that such…
Recently several authors have proved results on Ehrhart series of free sums of rational polytopes. In this note we treat these results from an algebraic viewpoint. Instead of attacking combinatorial statements directly, we derive them from…
We give a completely normal element in the maximal real subfield of a cyclotomic field over the field of rational numbers, which is different from that of Okada. This result is a consequence of the criterion for a normal element developed…
In this paper, we focus on the initial degree and the vanishing of the Valabrega-Valla module of a pair of monomials ideals $J\subseteq I$ in a polynomials ring over a field $\mathbb{K}$. We prove that the initial degree of this module is…
In this article we overview those aspects of the theory of affine semigroups and their algebras that have been relevant for our own research, and pose several open problems. Answers to these problems would contribute substantially to the…
Let C be a clutter and let A be its incidence matrix. If the linear system x>=0;xA<=1 has the integer rounding property, we give a description of the canonical module and the a-invariant of certain normal subrings associated to C. If the…
This paper concerns the exponentiation of monomial ideals. While it is customary for the exponentiation operation on ideals to consider natural powers, we extend this notion to powers where the exponent is a positive real number. Real…
We describe some basic facts about the weak subintegral closure of ideals in both the algebraic and complex-analytic settings. We focus on the analogy between results on the integral closure of ideals and modules and the weak subintegral…
Let $R$ be a local principal ideal ring of length two, for example, the ring $R=\Z/p^2\Z$ with $p$ prime. In this paper we develop a theory of normal forms for similarity classes in the matrix rings $M_n(R)$ by interpreting them in terms of…
Let $S = K[x_1, \ldots, x_n]$ denote the polynomial ring in $n$ variables over a field $K$ with each $\deg x_i = 1$ and $I \subset S$ a homogeneous ideal of $S$ with $\dim S/I = d$. The Hilbert series of $S/I$ is of the form…
The main purpose of this paper is to investigate prime, primary, and maximal ideals of semirings. The localization and primary decomposition of ideals in semirings are also studied.
We introduce a construction, called linearization, that associates to any monomial ideal $I$ an ideal $\mathrm{Lin}(I)$ in a larger polynomial ring. The main feature of this construction is that the new ideal $\mathrm{Lin}(I)$ has linear…
Let $D$ be an integrally closed domain with quotient field $K$. Let $A$ be a torsion-free $D$-algebra that is finitely generated as a $D$-module. For every $a$ in $A$ we consider its minimal polynomial $\mu_a(X)\in D[X]$, i.e. the monic…
In this paper, we discuss the normality of the toric rings of stable set polytopes, and the set of generators and Gr\"obner bases of toric ideals of stable set polytopes by using the results on that of edge polytopes of finite nonsimple…
Binomial ideals are special polynomial ideals with many algorithmically and theoretically nice properties. We discuss the problem of deciding if a given polynomial ideal is binomial. While the methods are general, our main motivation and…