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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.enter image description here

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?

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    Why is it not maximal?2012-01-16
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    "[$\ldots$] there exist[s] a maximal ideal of $A/a$ of the form $a+J$ [$\ldots$]". Ehm... I think you're using "$a$" here two mean two different things. Notice how the book you're quoting is using `\mathfrak` for ideals.2012-01-16

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