Abstract
We prove that, for each nonnegative integer n and n = ∞, there exists a compact topological space Ω such that the strict global dimension and the strict bidimension of the Banach algebra C(Ω) of all continuous functions on Ω are equal to n. We also obtain several “additivity formulas” for the strict homological dimensions of strict Banach algebras.
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Translated from Matematicheskie Zametki, vol. 80, no. 5, 2006, pp. 757–769.
Original Russian Text Copyright © 2006 by S. B. Tabaldyev.
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Tabaldyev, S.B. On strict homological dimensions of algebras of continuous functions. Math Notes 80, 715–725 (2006). https://doi.org/10.1007/s11006-006-0192-6
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DOI: https://doi.org/10.1007/s11006-006-0192-6