Geodesic
Additivity of Homological Dimensions for a Class of Banach Algebras
Funkcionalʹnyj analiz i ego priloženiâ, Tome 40 (2006) no. 3, pp. 93-95

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Let $\Omega$ 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 $\operatorname{dg}C(\Omega)\widehat{\otimes}B=\operatorname{dg}C(\Omega)+\operatorname{dg}B$ and $\operatorname{db}C(\Omega)\widehat{\otimes}B=\operatorname{db}C(\Omega)+\operatorname{db}B$ 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.
Mots-clés : global homological dimension, homological bidimension
Keywords: projective Banach module, metrizable compact space, derived set. 
@article{FAA_2006_40_3_a13,
     author = {S. B. Tabaldyev},
     title = {Additivity of {Homological} {Dimensions} for a {Class} of {Banach} {Algebras}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {93--95},
     publisher = {mathdoc},
     volume = {40},
     number = {3},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2006_40_3_a13/}
}
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S. B. Tabaldyev. Additivity of Homological Dimensions for a Class of Banach Algebras. Funkcionalʹnyj analiz i ego priloženiâ, Tome 40 (2006) no. 3, pp. 93-95. http://geodesic.mathdoc.fr/item/FAA_2006_40_3_a13/