Geodesic
Additivity of homological dimensions for tensor products of some Banach algebras
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2014), pp. 32-37 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is proved that if $A=C(\Omega)$, where $\Omega$ is an infinite metrizable compact space such that some finite-order iterated derived set of $\Omega$ is empty, then for every unital Banach algebra $B$ the global dimensions and the bidimensions of the Banach algebras $A\mathop{\widehat{\otimes}} B$ and $B$ are related by $\mathop{\mathrm{dg}} A\mathop{\widehat{\otimes}} B=2+\mathop{\mathrm{dg}} B$ and $\mathop{\mathrm{db}} A\mathop{\widehat{\otimes}} B=2+\mathop{\mathrm{db}} B$. Thus, a partial extension of Selivanov's result is obtained. 
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S. B. Tabaldyev. Additivity of homological dimensions for tensor products of some Banach algebras. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2014), pp. 32-37. http://geodesic.mathdoc.fr/item/VMUMM_2014_4_a4/

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