I have a very short question regarding the notation of an expectation term.
So in macroeconomics there is the Euler equation:
$$C^{-\sigma}_t=E_t\beta C^{-\sigma}_{t+1}(1+i_t)/(1+\pi_{t+1})$$
My question is now, would it be wrong if I notate it as follows: $$C^{-\sigma}_t=\beta E_tC^{-\sigma}_{t+1}(1+i_t)/(1+\pi_{t+1}).$$
Since $\beta$ is a constant and is not connoted with any uncertainty my guess would be that the two expressions above are actually the same and both notations would be correct.
Your assumption that the two terms are equivalent is correct. This property is called the linearity of the expectation. For a constant $a$ and two random variables $X,Y$ we have $E[aX] = aE[X]$ and $E[X+Y] = E[X]+E[Y]$. See the wiki page for more.