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On the completeness of Galois theories

Published online by Cambridge University Press:  09 April 2009

M. Venkataraman  and
T. Soundararajan
M. Venkataraman
Affiliation:
University of Madras Madurai, India
T. Soundararajan
Affiliation:
University of Madras Madurai, India
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Let E be a given field and G some (not necessarily the total) group of automorphisms of E. We introduce a topology in G by saying that a net of elements Tα in G converges to T in G if for each x∈E, Tα(x) coincides with Tα(x) ultimately. We shall call this the Krull topology on G.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 5 , Issue 3 , August 1965 , pp. 374 - 379
Copyright
Copyright © Australian Mathematical Society 1965

References

[1]Baer, R., A Galois theory of linear systems over commutative fields, Amer. J. Math. 62 (1940), 571.CrossRefGoogle Scholar
[2]Krull, W., Galoissche Theorie der unendlichen algebraischen Erweiterungen, Math. Ann. 100 (1928), 687–698.CrossRefGoogle Scholar
[3]Pickert, G., Einführung in die Höhere Algebra (Göttingen, 1951).Google Scholar
[4]Steinitz, E., Algebraische Theorie der Körper (New York, 1951).Google Scholar
[5]van der Waerden, B. L., Modern Algebra, Vol. I (New York, 1950).Google Scholar