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On q-Galois Extensions of Simple Rings

Published online by Cambridge University Press:  22 January 2016

Hisao Tominaga
Hisao Tominaga*
Affiliation:
Department of Mathematics, Hokkaido University
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In 1952, the late Professor T. Nakayama succeeded in constructing the Galois theory for finite dimensional simple ring extensions [7]. And, we believe, the theory was essentially due to the following proposition: If a simple ring A is Galois and finite over a simple subring B then A is B′-A-completely reducible for any simple intermediate ring B′ of A/B [7, Lemmas 1.1 and 1.2]. Moreover, as was established in [5], Nakayama’s idea was still efficient in considering the infinite dimensional Galois theory of simple rings.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 27 , Issue 2 , July 1966 , pp. 485 - 507
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

References

[1] Eilenberg, S. and Steenrod, N., Foundations of algebraic topology, Princeton (1952).Google Scholar
[2] Nagahara, T., On Galois conditions and Galois groups of simple rings, Trans. Amer. Math. Soc, 116 (1965), 417–434.Google Scholar
[3] Nagahara, T. and Tominaga, H., On Galois and locally Galois extensions of simple rings, Math. J. Okayama Univ., 10 (1961), 143–166.Google Scholar
[4] Nagahara, T. and Tominaga, H., On Galois theory of simple rings, Math. J. Okayama Univ., 11 (1963), 79–117.Google Scholar
[5] Nagahara, T. and Tominaga, H., Some theorems on Galois theory of simple rings, J. Fac. Sci. Hokkaido Univ., Ser. I, 17 (1963), 1–13.Google Scholar
[6] Nagahara, T. and Tominaga, H., On quasi-Galois extensions of division rings, J. Fac. Sci. Hokkaido Univ., Ser. I, 17 (1963), 73–78.Google Scholar
[7] Nakayama, T., Galois theory of simple rings, Trans. Amer. Math. Soc, 73 (1952), 276–292.Google Scholar
[8] Nobusawa, N. and Tominaga, H., On Galois theory of division rings III, Math. J. Okayama Univ., 10 (1960), 67–73.Google Scholar
[9] Tominaga, H., Galois theory of simple rings II, Math. J. Okayama Univ., 6 (1957), 153–170.Google Scholar
[10] Tominaga, H., On Nagahara’s theorem, J. Fac. Sci. Hokkaido Univ., Ser. I, 18 (1965), 153–157.Google Scholar