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Annihilator of tensor product when R$R$ is domain

Let R$R$ be a Noetherian domain and M$M$ and N$N$ be two faithful R$R$- modulesmodules. Is it true that Ann_R(M\otimes_R N)=0$\operatorname{Ann}_R(M\otimes_R N)=0$?

Annihilator of tensor product when R is domain

Let R be a Noetherian domain and M and N be two faithful R- modules. Is it true that Ann_R(M\otimes_R N)=0?

Annihilator of tensor product when $R$ is domain

Let $R$ be a Noetherian domain and $M$ and $N$ be two faithful $R$-modules. Is it true that $\operatorname{Ann}_R(M\otimes_R N)=0$?

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Annihilator of tensor product when R is domain

Let R be a Noetherian domain and M and N be two faithful R- modules. Is it true that Ann_R(M\otimes_R N)=0?