13 April 2010 2:30 - 4:00 R Raphael
Commutative pm rings

We limit the discussion to commutative rings. A ring R is called pm if each prime ideal lies in only one maximal ideal. The class is limited but natural as evidenced by examples we give.
We present in detail a beautiful theorem due to DeMarco and Orsatti that characterizes these rings.

Thm The following are equivalent.

  1. R is pm
  2. Spec R is normal
  3. Max R is a retract of Spec R.
Under these circumstances the map from Spec R to Max R is continuous.