Let $M$ be a module over a commutative ring $R$, $\mathfrak a$ is an ideal of $R$.
Define $\Gamma_\mathfrak a(M)=\lbrace m\in M\mid\mathfrak a^tm=0 \text{ for some } t\in \mathbb{N}\rbrace$.
Then $\Gamma_\mathfrak a$ is a functor (from the category $R-\operatorname{mod}$ to $R-\operatorname{mod}$). Some textbook in commutative algebra claimed that $\Gamma_\mathfrak a$ is left exact but not right exact, but I could not prove that.
Please help me to prove and better help me to find an example that $\Gamma_\mathfrak a$ is not right exact.
Edit. Thanks to the answer of YACP, but I think I should make my question more precise:
Suppose that I have an exact sequence of the form $0\rightarrow N\rightarrow M\rightarrow P\rightarrow 0$. After taking the action of $\Gamma_{\mathfrak{a}}$, why we can not get a short exact sequence $0\rightarrow \Gamma_{\mathfrak{a}}(N)\rightarrow \Gamma_{\mathfrak{a}}(M)\rightarrow \Gamma_{\mathfrak{a}}(P)\rightarrow 0$ ? Why is it not exact at $\Gamma_{\mathfrak{a}}(P)\rightarrow 0$?