In this appendix we summarize briefly some of the algebra needed in the rest of the book. We give proofs in general only for those results which we have not found stated conveniently in one of the main references: otherwise we give a reference to one or more of the standard texts on the subject.

We have included some results which are not used in the rest of the book. In some cases this is intended to put those results which are needed into a more general context. But we have included also a section on Cohen-Macaulay rings and modules: this is intended to make it easier to read certain works on tranformation groups where Cohen-Macaulay theory is used. See, e.g., [Allday, 1979], [Atiyah, 1974], [Bredon, 1974] and [Duflot, 1981]. See also Section 5.5.

On the other hand there are some very useful topics which we have not included. Three which spring to mind are:

1. Noether's Normalization Lemma: see e.g., [Serre, 1965a], Chapter III, Théorème 2;

2. The going up and going down (Cohen-Seidenberg) theorems: see e.g., [Matsumura, 1986], §9, or [Serre, 1965a], Chapter III, part A; and

3. Preparation theorems, Grauert invariants, Gröbner bases, etc.: see e.g., [Chang, Su, 1980].