Algebraic extension of normed algebras

Abstract

in B. The classical method of field extension (forming the polynomial ring A [x] and reducing modulo the principal ideal J of 1.1) solves this problem. In this paper, we investigate the role of this process in topological rings. We study the problem of obtaining a normed linear algebra extension B containing a solution of 1.1, where A is a given normed linear algebra. Our method is to define a norm first in the polynomial algebra A [x], and to do it in such a way that J is closed (for otherwise the canonical norm in