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On Certain Extensions of Function Rings

Published online by Cambridge University Press:  20 November 2018

Bernhard Banaschewski
Bernhard Banaschewski*
Affiliation:
Hamilton College McMaster University
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The present note is concerned with the existence and properties of certain types of extensions of Banach algebras which allow a faithful representation as the normed ring C(E) of all bounded continuous real functions on some topological space E. These Banach algebras can be characterized intrinsically in various ways (1); they will be called function rings here. A function ring E will be called a normal extension of a function ring G if E is directly indecomposable, contains C as a Banach subalgebra and possesses a group G of automorphisms for which C is the ring of invariants, that is, the set of all elements fixed under G. G will then be called a group of automorphisms of E over C. If E is a normal extension of C with precisely one group of automorphisms over C, which is then the invariance group of C in E, then E will be called a Galois extension of C. Such an extension will be called finite if its group is finite.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 11 , 1959 , pp. 87 - 96
Copyright
Copyright © Canadian Mathematical Society 1959

References

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