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A characterization of determinants over topological fields

Published online by Cambridge University Press:  18 May 2009

R. W. K. Odoni
R. W. K. Odoni
Affiliation:
University of Glasgow, Glasgow G12 8QQ
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Let K be a topological field. On introducing the vector-space topology on the n × n matrices over K, it becomes clear that the determinant map φ enjoys the following properties:

(A) φ is a continuous surjective homomorphism from GLn(K) to K*,

(B) φ(μa) = μn φ(a) for each non-zero φ in K, and all a in GLn(K).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 15 , Issue 1 , March 1974 , pp. 60 - 62
Copyright
Copyright © Glasgow Mathematical Journal Trust 1974

References

REFERENCES

1.Hensel, K., Über den Zusammenhang zwischen den Systemen und ihren Determinanten, J. Reine Angew. Math. 159 (1928), 240–254.Google Scholar
2.Artin, E. and Tate, J. T., Class-field theory (New York, 1967), p. xi.Google Scholar
3.Neukirch, J., Klassenkörpertheorie (Mannheim, 1969).Google Scholar