Geodesic
Unramified algebraic extensions of commutative Banach algebras
Sbornik. Mathematics, Tome 20 (1973) no. 3, pp. 419-437

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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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     author = {Yu. V. Zyuzin and V. Ya. Lin},
     title = {Unramified algebraic extensions of commutative {Banach} algebras},
     journal = {Sbornik. Mathematics},
     pages = {419--437},
     publisher = {mathdoc},
     volume = {20},
     number = {3},
     year = {1973},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1973_20_3_a6/}
}
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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/