Abstract
Let Ω be a metrizable compact space. Suppose that its derived set of some finite order is empty. Let B be a unital Banach algebra, and let \(\widehat \otimes \) stand for the projective tensor product. We prove the additivity formulas dg C(Ω)B\(\widehat \otimes \)=dgB and db C(Ω)\(\widehat \otimes \)B=dbC(Ω)+dbB for the global homological dimension and the homological bidimension. Thus these formulas are true for a new class of commutative Banach algebras in addition to those considered earlier by Selivanov.
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