Tagged Questions

The tag has no usage guidance.

77 views

How to compute graph ideal or cut ideal of a graph?

Graph ideals are a special case of Stanley-Reisner ideal, explained in Combinatorial Commutative Algebra book by Sturmfels, and graph ideals here. Graph ideals are generated by the minimal paths while ...
67 views

Cut ideal of two graphs?

Consider a connected graph $G$ and a connected graph $H$. Their graph ideals are their path ideals. The Alexander duality of the graph ideals give the cut ideals. $G$ and $H$ are not connected to each ...
187 views

A property of minimal prime ideals in commutative reduced ring

Let $\{\mathfrak{p}_i\}_{i\in I}$ ($I$ is an infinite set) be a family of minimal prime ideals in a commutative reduced ring $R$ with identity, and let $a, b \in R$. If the ideal $\langle a, b\rangle$...
38 views

Ideals of finite codimension in $L^1(G)$

Let $G$ be a non-abelian, locally compact group. Is there any characterization of the two-sided ideals of $L^1(G)$ which are of finite codimension?
124 views

An ideal and its annihilator

Let $I$ be an arbitrary ideal of commutative ring $R$ with identity. If $ann (I)=AB$, where $A$ and $B$ are comaximal, how can we fine two ideal $I_1$ and $I_2$ with $I=I_1+I_2$ such that $I_1$ ...
66 views

How are Polynomials of Toric ideals Studied with Exponents as ST-cuts?

Topic: Toric ideals on Expected value of Structure Functions in Random Graphs Goal: to understand the toric ideal where the exponents $h_i$ and $s_j$ are st-vertex-cuts of a digraph ...
I want to understand in what sense topology is dual to bornology at a most basic level. Therefore, I rephrased the definition of a bornology in the following way: Let $X$ be a set and let $\mathcal{P}... 0answers 86 views $T$-nilpotent ideals Recall that a subset$I$of a ring$R$is left (resp., right)$T$-nilpotent in case for every sequence $$a_1,a_2,\cdots$$ in$I$there is an$n$such that$a_1\cdots a_n=0$(resp.,$a_n\cdots a_1=0$).... 0answers 60 views some sort of 'saturation' of module quotients Let$R$be a local Noetherian ring over a field, with the maximal ideal$\mathfrak{m}$. (e.g.$R=k[[x_1,\dots,x_{p>1}]]$) Given two$R$-modules,$N\subset M$, of the same (finite, non-zero) rank. ... 0answers 104 views Can it occur that$q^{ce}$is a prime ideal (of$S$), while$q^{ce}\neq q $? Let$R$and$S$be commutative rings (with$1$) and$f : R\to S$be a ring homomorphism. For an ideal$I$of$R$, set$I^e:=\langle f(I)S\rangle$(called the extension of$I$to$S$) and for an ideal$...
Let $R$ and $S$ be commutative rings (with $1$), and $f : R\to S$ be a ring homomorphism. For an ideal $I$ of $R$, set $I^e:=\langle f(I)S\rangle$ (called the extension of $I$ to $S$). When $f$ is ...