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Hello All,is This conclusion true? If $(R,m)$ is a local ring and $ Min Ass R=Ass R$ then can we conclude that $Min Ass \hat{R}=Ass \hat{R}$? ($\hat{R}$ is $m$-adic completion of $R$) $MinAss …

Possible Duplicate: minimal prime devisor(MinAss R) Hello All,is This conclusion true? $(R,m)$ be a local ring.if every associated prime ideal of $R$ be minimal then every associated prime i …

You can see Theorem 18.6 in Commutative ring theory by H.Matsumura.

We know that a finitely generated $R$-module $M$ satisfies the $(S_n)$ condition if $$\operatorname{depth} M_p \geq \min(n,\dim M_p)$$ for every $p\in \operatorname{Spec}R$. It's well known that Cohe …

Is it true that: Let $R$ be a local ring and $\dim R= d$. If $b\subset a$ be two proper ideals of $R$ then for $ n\in {\Bbb N}$, $\varinjlim Ext^d_R(a^n/b^n,R)=0$

Let $R$ be a noetherian ring and $M$ , $N$ be finitely generated $R$-modules. Then what is the relation between $Ass\ Ext^i_R(M,N)$ and $Ass\ M, Ass\ N$? $Ass$ means set of associated prime ideals. …

Let $\hat{R}$ is $m$-adic completion of a local ring $(R,m)$.What is the relation between $Min R$ and $Min \hat{R}$. we know that $\hat{R}$ is faithfully flat $R$-module. $Min R$=set of all minimal p …

we know that the maximal ideals of ${\mathbb Z}[x]$ are of the form $(p, f(x))$ where $p$ is a prime number and $f(x)$ is a polynomial in ${\mathbb Z}[x]$ which is irreducible modulo $p$. Is it true …