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### 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?
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### 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 $I_1$ ...
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### 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.,$a_n\cdots a_1=0$).... 1answer 148 views ### In what conditions every ideal is an extension ideal? Is every prime ideal extension of prime 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 ... 0answers 101 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 $R$ 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. ...