Geodesic
Unramified algebraic extensions of commutative Banach algebras
Sbornik. Mathematics, Tome 20 (1973) no. 3, pp. 419-437 
Yu. V. Zyuzin; V. Ya. Lin. Unramified algebraic extensions of commutative Banach algebras. Sbornik. Mathematics, Tome 20 (1973) no. 3, pp. 419-437. http://geodesic.mathdoc.fr/item/SM_1973_20_3_a6/
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     title = {Unramified algebraic extensions of commutative {Banach} algebras},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Extensions of a commutative Banach algebra $A$ by means of roots of polynomials over $A$ with invertible discriminant are investigated. In the case when $A$ has no nontrivial idempotent, for each such polynomial $f$ a Banach algebra $A_f$, which plays the role of a minimal splitting algebra, is constructed. Unramified radical extensions of $A$ are defined, and the question of the solvability of algebraic equations over $A$ in unramified radicals is investigated. Bibliography: 12 titles.

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[4] Yu. V. Zyuzin, “Algebraicheskie uravneniya s nepreryvnymi koeffitsientami na odnorodnykh prostranstvakh”, Vestnik MGU, 1972, no. 1, 51–53 | Zbl

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[7] D. T. Brown, “Galois theory for Banach algebras”, Pacific J. Math., 30:3 (1969), 577–600 | MR | Zbl

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[9] L. Khermander, Vvedenie v teoriyu funktsii neskolkikh kompleksnykh peremennykh, izd-vo «Mir», Moskva, 1968 | MR

[10] Kh. Roiden, “Funktsionalnye algebry”, Matematika, 9:2 (1965)

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[12] R. Fox, L. Neuwirth, “The braid groups”, Math. Scand., 10:1 (1962), 119–126 | MR | Zbl