Depth of C(X)-modules

Abstract

It is shown that the depth of every module over C(X), the ring of all real valued continuous functions on a topological space X, is at most 1. This result is proved for modules over rings of a much more general class than the rings of continuous functions. It also turns out that many facts in the literature concerning the depths of C(X), their sub-algebras, and ideals are consequences of this main result. Some known results are generalized and some applications are given.