The Index of Reducibility of Parameter Ideals in Low Dimension

The Index of Reducibility of Parameter Ideals and Mostly Zero Finite Local Cohomologies

In this paper we prove that ifM is a finitely-generated module of dimension d with finite local cohomologies over a Noetherian local ring (A,m), and if Him (M) = 0 except possibly for i ∈ {0, r, d} with some 0 ≤ r ≤ d, then there exists an integer l such that every parameter ideal for M contained in m has the same index of reducibility. This theorem generalizes earlier work of the second author...

On One-Sided Ideals of Rings of Linear Transformations

Adjacency metric dimension of the 2-absorbing ideals graph

Let Γ=(V,E) be a graph and ‎W_(‎a)={w_1,…,w_k } be a subset of the vertices of Γ and v be a vertex of it. The k-vector r_2 (v∣ W_a)=(a_Γ (v,w_1),‎…‎ ,a_Γ (v,w_k)) is the adjacency representation of v with respect to W in which a_Γ (v,w_i )=min{2,d_Γ (v,w_i )} and d_Γ (v,w_i ) is the distance between v and w_i in Γ. W_a is called as an adjacency resolving set for Γ if distinct vertices of ...

On ideals of ideals in $C(X)$

In this article‎, ‎we have characterized ideals in $C(X)$ in which‎ ‎every ideal is also an ideal (a $z$-ideal) of $C(X)$‎. ‎Motivated by‎ ‎this characterization‎, ‎we observe that $C_infty(X)$ is a regular‎ ‎ring if and only if every open locally compact $sigma$-compact‎ ‎subset of $X$ is finite‎. ‎Concerning prime ideals‎, ‎it is shown that‎ ‎the sum of every two prime (semiprime) ideals of e...

Local Cohomology with Respect to a Cohomologically Complete Intersection Pair of Ideals

Let $(R,fm,k)$ be a local Gorenstein ring of dimension $n$. Let $H_{I,J}^i(R)$ be the  local cohomology with respect to a pair of ideals $I,J$ and $c$ be the $inf{i|H_{I,J}^i(R)neq0}$. A pair of ideals $I, J$ is called cohomologically complete intersection if $H_{I,J}^i(R)=0$ for all $ineq c$. It is shown that, when $H_{I,J}^i(R)=0$ for all $ineq c$, (i) a minimal injective resolution of $H_{I,...