Related papers: Two ideals connected with strong right upper poros…

A homogeneous ideal $I$ of a polynomial ring $S$ is said to have the Rees property if, for any homogeneous ideal $J \subset S $ which contains $I$, the number of generators of $J$ is smaller than or equal to that of $I$. A homogeneous ideal…

We give a method for constructing principal ideals in spaces of real functions whose intersection is not a finitely generated ideal. This problem is also discussed for spaces of holomorphic functions.

Let $\ast $ be a star operation of finite character. Call a $\ast $-ideal $I$ of finite type a $\ast $-homogeneous ideal if $I$ is contained in a unique maximal $\ast $-ideal $M=M(I).$ A maximal $\ast $-ideal that contains a $\ast…

Given a unital associative ring S and a subring R, we say that S is an ideal (or Dorroh) extension of R if for some ideal I of S, S = R + I, where the sum is direct. In this note we investigate the ideal structure of an arbitrary ideal…

The core of an $R$-ideal $I$ is the intersection of all reductions of $I$. This object was introduced by D. Rees and J. Sally and later studied by C. Huneke and I. Swanson, who showed in particular its connection to J. Lipman's notion of…

Answering questions raised in \cite{Leonetti, Uzcategui} we characterize ideals $\mathcal I\subseteq \mathcal P(\omega)$ such that $c_{0,\mathcal I}$ is complemented in $\ell_\infty$ as exactly those ideals for which the space $K_{\mathcal…

Let $E$ be an arbitrary directed graph and let $L$ be the Leavitt path algebra of the graph $E$ over a field $K$. It is shown that every ideal of $L$ is an intersection of primitive/prime ideals in $L$ if and only if the graph $E$ satisfies…

If $G$ is a finite Coxeter group, then symplectic reflection algebra $H:=H_{1,\eta}(G)$ has Lie algebra $\mathfrak {sl}_2$ of inner derivations and can be decomposed under spin: $H=H_0 \oplus H_{1/2} \oplus H_{1} \oplus H_{3/2} \oplus ...$.…

Given an arbitrary spectral space $X$, we endow it with its specialization order $\leq$ and we study the interplay between suprema of subsets of $(X,\leq)$ and the constructible topology. More precisely, we investigate about when the…

The second Veronese ideal $I_n$ contains a natural complete intersection $J_n$ generated by the principal $2$-minors of a symmetric $(n\times n)$-matrix. We determine subintersections of the primary decomposition of $J_n$ where one…

Given an ideal $I$ on $\omega$ let $a(I) $ ($\bar{a}(I)$) be minimum of the cardinalities of infinite (uncountable) maximal $I$-almost disjoint subsets of $[{\omega}]^{\omega}$, and denote $b_I$ and$d_I$ the unbounding and dominating…

In this paper, we define the concept $I-$prime hyperideal in a multiplicative hyperring $R$. A proper hyperideal $P$ of $R$ is an $I-$prime hyperideal if for $a, b \in R$ with $ab \subseteq P-IP$ implies $a \in P$ or $b \in P$. We provide…

Can there be a structure space-type theory for an arbitrary class of ideals of a ring? The ideal spaces introduced in this paper allows such a study and our theory includes (but not restricted to) prime, maximal, minimal prime, strongly…

Given a symbolic power of a homogeneous ideal in a polynomial ring, we study the problem of determining which powers of the ideal contain it. For ideals defining 0-dimensional subschemes of projective space, as an immediate corollary of our…

Suppose $\mathcal I$ and $\mathcal J$ are proper ideals on some set $X$. We say that $\mathcal I$ and $\mathcal J$ are incompatible if $\mathcal I \cup \mathcal J$ does not generate a proper ideal. Equivalently, $\mathcal I$ and $\mathcal…

Let $H$ be an open subgroup of a profinite group that can be expressed as intersection of maximal subgroups of $G.$ Given a positive real number $\eta,$ we say that $H$ is an $\eta$-intersection if there exists a family of maximal subgroups…

As a natural extension of the ongoing development of a theory of ideals in commutative quantales with an identity element, this article aims to study into the analysis of certain topological properties exhibited by distinguished classes of…

For the family of graded lattice ideals of dimension 1, we establish a complete intersection criterion in algebraic and geometric terms. In positive characteristic, it is shown that all ideals of this family are binomial set theoretic…

The goal of this short note is to prove that when $A$ is a closed *-subalgebra of a C*-algebra $B$ satisfying the ideal intersection property plus a mild axiom (INV), then the map $J\mapsto J\cap A$ establishes an isomorphism from the…

Let $R = \mathbb{K}[x_1, \ldots, x_n]$ and $I \subset R$ be a homogeneous ideal. In this article, we first obtain certain sufficient conditions for the subadditivity of $R/I$. As a consequence, we prove that if $I$ is generated by…