The prime ideal is a princess of the world of ideals. Her father is the prince 'Point' in the world of geometry. Her mother is the princess 'Prime Numbers' in the world of numbers. She inherits the purity from her parents.
KatoI'm a young guy called 'commutative ring', but I was originally 'the ring of continuous functions on a compact Hausdorff space'. Now I am an algebraic object, so I must say goodbye to my home village, the space, but I will always keep it in my heart as a set of maximal ideals.
KatoIt never happens that, when we go home and open the refrigerator, we see all infinitely many prime numbers there.
Kato