Algebraic Extensions of Normed Algebras

Details Algebraic Extensions of Normed Algebras Algebraic Extensions of Normed Algebras

2001-02-16

arxiv.org/abs/math/0102131v1

Mathematics

Functional Analysis

TeX. 47 pages, 0 figures. M.Math Dissertation, University of Nottingham, academic year 1999-2000

Scientific paper

We compare two known methods of extending a complex, unital, commutative normed algebra so as to include solutions to sets of monic polynomials over the original algebra. (One of these is a generalisation of a construction from the thesis of B. J. Cole and only applies to uniform algebras.) An example is given to show that they can lead to essentially different algebras. Integrally closed extensions which generalise Cole's `universal root algebras' are also constructed .

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