chapter  18
11 Pages

Unmixedness and the Generalized Principal Ideal Theorem

ByTracy Dawn Hamilton

In two recent papers ([1] and [2]) we have studied wB-ht-unmixed rings and wBunmixed rings as candidates for an appropriate definition of non-Noetherian CohenMacaulayness. The question of whether there exists an appropriate definition of non-Noetherian Cohen-Macaulayness was first posed by Sarah Glaz in 1992 [3] and then again in 1994 [4]. WB-ht-unmixedness and wB-unmixedness (which will be defined in Section 2) have each been shown to satisfy, at least, some of the requirements for an appropriate definition of non-Noetherian Cohen-Macaulayness.