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$N$ and $K$ are submodules of $M$ with $I=Ann(N)$ and $J=Ann(K)$, then show that annihilator of intersection of $N$ and $K$ contains $I+J$. Give example to show that the inclusion may be strict.

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marked as duplicate by rschwieb, Community, Andrew D. Hwang, Lost1, Shuchang Feb 28 '14 at 0:53

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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It looks like you are new to MSE, so I will welcome you :) hi! On MSE we love to help people but we don't want to work for them, so we appreciate it when questions are asked with a little explanation as to where the person asking the question is stuck. Have you done any progress on the question? Where are you stuck? – Patrick Da Silva Jan 2 '13 at 13:38

Hint: How do you usually prove inclusion? you should start by picking $i\in I$ and $j\in J$. For any $m\in N\cap K$, $im=0$ and $jm=0$ (why?), so what can you conclude about $i+j$?
What happens when $N\cap K=(0)$?

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