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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