This article is cited in 4 papers

Unramified algebraic extensions of commutative Banach algebras

Yu. V. Zyuzin, V. Ya. Lin


Abstract: 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.

UDC: 519.56

MSC: Primary 46J05, 13B05; Secondary 13B25

Received: 31.10.1972

 English version: Mathematics of the USSR-Sbornik, 1973, 20:3, 419–437

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