FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2001, VOLUME 7, NUMBER 4, PAGES 1037-1046

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

A. V. Kuzmin

Abstract

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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 $I$Ì C(X) as left modules and bimodules.

All articles are published in Russian.

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Last modified: April 17, 2002