Additivity of homological dimensions for a class of Banach algebras

Author： Tabaldyev S.  

Publisher： Springer Publishing Company

ISSN： 0016-2663

Source： Functional Analysis and Its Applications, Vol.40, Iss.3, 2006-07, pp. : 244-246

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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 stand for the projective tensor product. We prove the additivity formulas dg C(Ω)B =dgB and db C(Ω) 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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