Let $N$ and $K$ be sub-modules of $M$ with $I=\operatorname{Ann}(N)$ and $J=\operatorname{Ann}(K)$. Show that $I+J$ is a proper subset of $\operatorname{Ann}(N \cap K)$.
Let $N$, $K$ be sub-modules of $M$ with $I=\mathrm{Ann}(N)$, $J=\mathrm{Ann}(K)$. Show $I+J$ is a proper subset of $\mathrm{Ann}(N \cap K)$.
1
$\begingroup$
modules
-
0When $N=K$, for example, there's equality $I+J= \text{Ann}(N\cap K)$. Perhaps the word "proper" is redundant? – 2012-12-31