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Groups, Coverings and Galois Theory

Published online by Cambridge University Press:  20 November 2018

Vagn Lundsgaard Hansen  and
Peter Petersen V
Vagn Lundsgaard Hansen
Affiliation:
Mathematical Institute, The Technical University of Denmark, Building 303, DK-2800 Lyngby, Denmark
Peter Petersen V
Affiliation:
Department of Mathematics, University of California, Los Angeles, CA 90024, U. S. A.
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Abstract

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Finite extensions of complex commutative Banach algebras are naturally related to corresponding finite covering maps between the carrier spaces for the algebras. In the case of function rings, the finite extensions are induced by the corresponding finite covering maps, and the topological properties of the coverings are strongly reflected in the algebraic properties of the extensions and conversely. Of particular interest to us is the class of finite covering maps for which the induced extensions of function rings admit primitive generators. This is exactly the class of polynomial covering maps and the extensions are algebraic extensions defined by the underlying Weierstrass polynomials.

The purpose of this paper is to develop a suitable Galois theory for finite extensions of function rings induced by finite covering maps and to apply it in the case of Weierstrass polynomials and polynomial covering maps.

Keywords

57M1213B2546J10
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 43 , Issue 6 , 01 December 1991 , pp. 1281 - 1293
Copyright
Copyright © Canadian Mathematical Society 1991

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