Sorry for asking this simple things... First I will put the results that are used. I have a stupid question about the proof of the corollary.
I don´t know totally how to use the proposition 1.1, because I can guarantee that there exist a maximal ideal of $ A/a $ of the form $ a+J $ using the hint. And now? clearly it´s natural in consider the preimage of the projection $\pi^{-1}(a+J)$ since it is an ideal of A , but not necessarily a maximal ideal. So what can I do?