I begin to study the *operator on the domain, maybe I do not choose a perfect book which contains many theorems but no enough examples, if you know some good reference, recomment it to me please.
Now let us match the *operator with the ideal, we can get two concepts: the maximal *ideal(the maximal element of the *ideal) and * maximal ideal(*ideal and also maxiaml ideal). Here are my questions:
1) Obviously, a *maximal ideal must be a maximal *ideal, but does a maximal *ideal must be a *maximal ideal? If not, does it must be prime?
2) For any domain, does maximal *ideal or *maximal ideal must be exist?