Maximal *ideal and *maximal ideal - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T21:06:36Z http://mathoverflow.net/feeds/question/114969 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/114969/maximal-ideal-and-maximal-ideal Maximal *ideal and *maximal ideal Strongart 2012-11-30T11:40:17Z 2012-11-30T13:26:14Z <p>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.</p> <p>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:</p> <p>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?</p> <p>2) For any domain, does maximal *ideal or *maximal ideal must be exist?</p>