zbMATH — the first resource for mathematics

Homological dimensions of \(C(\Omega)\)-modules. (English. Russian original) Zbl 0992.46063
Mosc. Univ. Math. Bull. 55, No. 4, 32-35 (2000); translation from Vestn. Mosk. Univ., Ser. I 2000, No. 4, 52-55 (2000).
Let \(C(\Omega)\) be an algebra of continuous functions on the compactum \(\Omega\) with regular Borel measure \(\mu\). The author studies the properties of the unital Hilbert module over \(C(\Omega)\). The analysis of projectivity conditions of both the Hilbert module and the unital Hilbert module [A. Ya. Khelemskij, “Homology in Banach and topological algebras”, Moscow, Izdatel’stvo Moskovskogo Gosudarstvennogo Universiteta (1986; Zbl 0608.46046)] is presented.
46M18 Homological methods in functional analysis (exact sequences, right inverses, lifting, etc.)
46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
55N35 Other homology theories in algebraic topology
55N15 Topological \(K\)-theory
55M10 Dimension theory in algebraic topology
54C35 Function spaces in general topology
54F45 Dimension theory in general topology