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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.
##### MSC:
 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