Geodesic
Homological dimension of Banach algebras of analytic functions
Sbornik. Mathematics, Tome 12 (1970) no. 2, pp. 221-233 
A. Ya. Helemskii. Homological dimension of Banach algebras of analytic functions. Sbornik. Mathematics, Tome 12 (1970) no. 2, pp. 221-233. http://geodesic.mathdoc.fr/item/SM_1970_12_2_a4/
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     author = {A. Ya. Helemskii},
     title = {Homological dimension of {Banach} algebras of analytic functions},
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     volume = {12},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1970_12_2_a4/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this article we calculate the homological dimensions of a certain class of Banach modules over algebras with uniform convergence. The scheme proposed allows us, in particular, to find the homological dimension of all one-dimensional modules over Banach algebras of functions holomorphic on a polydisk and on a ball in $\mathbf C^n$. Bibliography: 7 titles.

[1] E. Hewitt, “The ranges of certain convolution operators”, Math. Scand., 15 (1964), 147–155 | MR | Zbl

[2] E. M. Glison, “Konechno-porozhdennye idealy v banakhovykh algebrakh”, Matematika, 9:4 (1965), 119–127

[3] M. M. Dei, Normirovannye lineinye prostranstva, IL, Moskva, 1961

[4] A. Kartan, S. Eilenberg, Gomologicheskaya algebra, IL, Moskva, 1960

[5] S. Maklein, Gomologiya, Mir, Moskva, 1966

[6] M. A. Naimark, Normirovannye koltsa, Fizmatgiz, Moskva, 1968 | MR

[7] A. Ya. Khelemskii, “O gomologicheskoi razmernosti normirovannykh modulei nad banakhovymi algebrami”, Matem. sb., 81(123) (1970), 430–444