Krull Dimension, Depth, and Width

A fundamental idea in commutative algebra is to link a module with particular subsets of the prime ideal spectrum of the ring. The study of these sets and the information they capture goes by the name of support theories. The classic support of a module, with its subsets of minimal and associated prime ideals, was already recalled in Sect. 12.4. The next chapter covers more modern notions of support that conform better to derived category methods, but here we are concerned with the classic notion. In the first sections it is extended to complexes along with the related numerical invariant: the Krull dimension. Later sections extend the classic notion of depth, and the dual notion of width, to complexes.