On Nagata’s Result about Height One Maximal Ideals and Depth One Minimal Prime Ideals (II)

We expand the theory of height one maximal ideals and depth one minimal prime ideals initiated by M. Nagata and continued by the authors in part I. A local ring is doho in case its completion has at least one depth one minimal prime ideal. We establish several families of doho local rings, prove that certain local rings associated with Rees valuation rings are doho, and complement a famous construction of Nagata by proving that each doho local domain (<I>R,M</I>) of altitude α ≥ 2 has a quadratic integral extension over-domain with precisely two maximal ideals, one of height α and the other of height one.