Additivity of homological dimensions for tensor products of some Banach algebras / S. B. Tabaldyev. //Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2014. № 4. P. 32-37 [Moscow Univ. Math. Bulletin. Vol. 69, N 4, 2014.].
It is proved that if A=C(Ω), where Ω is an infinite metrizable compact space such that some finite-order iterated derived set of Ω is empty, then for every unital Banach algebra B the global dimensions and the bidimensions of the Banach algebras A⨶B and B are related by dg A⨶B=2+dg B and db A⨶B=2+db B. Thus, a partial extension of Selivanov's result is obtained.
Key words: Banach module, homological dimension, global dimension, bidimension.