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Non-Normal Galois Theory forNon-Commutative and Non-semisimple Rings

Published online by Cambridge University Press:  20 November 2018

Tadasi Nakayama
Tadasi Nakayama*
Affiliation:
Nagoya University
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The purpose of the present work is to give, as a continuation of the writer's study of Galois theory for general rings ([8], [9], [10]), a kind of Galois theory for general, non-commutative and non-semisimple rings, which includes, at least in its main features, the Kaloujnine-Jacobson Galois theory of non-normal fields ([3]; cf. [4], [5]). To deal with the non-commutativity we bring to the fore certain double-moduli rather than self-composites, while the non-semisimplicity is manipulated by the method and idea used in the writer's above mentioned study on (normal) Galois theory and commuter systems of nonsemisimple rings. (For the normal Galois theory of rings cf. [1], [2], [6], [7], [11], besides the above.) Some of our arguments may even serve to make some simplification in Jacobson's treatment of ordinary fields.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 3 , 1951 , pp. 208 - 218
Copyright
Copyright © Canadian Mathematical Society 1951

References

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