On the homological dimension of normed modules over Banach algebras
Sbornik. Mathematics, Tome 10 (1970) no. 3, pp. 399-411 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this work there is introduced a notion of relative homological dimension of a normed module over a Banach algebra. This dimension is computed for several cases. The results obtained are applicable to finding cohomology groups of certain Banach algebras and to solving the question of the strong decomposability of certain classes of extended Banach algebras. Bibliography: 13 titles.
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     title = {On~the homological dimension of normed modules over {Banach} algebras},
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A. Ya. Helemskii. On the homological dimension of normed modules over Banach algebras. Sbornik. Mathematics, Tome 10 (1970) no. 3, pp. 399-411. http://geodesic.mathdoc.fr/item/SM_1970_10_3_a6/

[1] W. G. Bade, P. C. Curtis, “The Wedderburn decomposition of commutative Banach algebras”, Amer. J. Math., 82:4 (1960), 851–866 | DOI | MR | Zbl

[2] S. Eilenberg, J. C. Moore, “Foundations of the relative homological algebra”, Mem. Amer. Math. Soc., 1965, no. 55 | MR

[3] A. Grothendieck, “Produits tensoriels topologiques et espaces nucleaires”, Mem. Amer. Math. Soc., 1955, no. 16, 3–191 | MR

[4] A. Guichardet, “Sur l'homologie et la cohomologie des algebres de Banach”, C. R. Acad. Sci., 262 (1966), 38–41, Paris | MR | Zbl

[5] G. Hochschild, “On the cohomology theory for an associative algebras”, Ann. Math., 47:3 (1946), 568–679 | DOI | MR

[6] H. Kamowitz, “Cohomology groups of commutative Banach algebras”, Trans. Amer. Math. Soc., 102 (1962), 352–372 | DOI | MR | Zbl

[7] C. E. Rickart, The general theory of Banach algebras, D. Van Nostrand, Princeton New York, 1960 | MR | Zbl

[8] S. Maiklen, Gomologiya, Mir, Moskva, 1966

[9] B. S. Mityagin, A. S. Shvarts, “Funktory v kategoriyakh banakhovykh prostranstv”, Uspekhi matem. nauk, XIX:2(116) (1964), 66–130

[10] A. Ya. Khelemskii, “Annulyatornye rasshireniya kommutativnykh banakhovykh algebr”, Izv. AN SSSR, seriya matem., 29 (1965), 945–956

[11] A. Ya. Khelemskii, “Silnaya razlozhimost konechnomernykh rasshirenii $C^*$-algebr”, Vestnik MGU, seriya matem., mekh., 1967, no. 4, 50–52

[12] A. Ya. Khelemskii, “O singulyarnykh rasshireniyakh algebry vsekh nepreryvnykh funktsii na kompakte”, Sib. matem. zh., 1969, no. 3, 671–684

[13] I. Dugundji, “An extension of Tietzés theorem”, Pacific J. Math., 1:3 (1951), 353–367 | MR | Zbl