Homological properties of algebra $C(X)$ in non-Archimedean analysis

In this article the author offers a variant of homological theory in non-Archimedean analysis and computes the left global dimension and bidimension of an algebra $C(X)$ of all continuous functions on an ultrametrizable compact set $X$. To the moment the analogous problem in Archimedean analysis is still not solved. More generally, the author computes the homological dimensions of ideals $I\subset C(X)$ as left modules and bimodules.