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On a classification of the function fields of algebraic tori

Published online by Cambridge University Press:  22 January 2016

Shizuo Endo  and
Takehiko Miyata
Shizuo Endo
Affiliation:
Tokyo Metropolitan University, Osaka City University
Takehiko Miyata
Affiliation:
Tokyo Metropolitan University, Osaka City University
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Let II be a finite group and denote by MII the class of all (finitely generated Z-free) II-modules. In the previous paper [3] we defined an equivalence relation in MII and constructed the abelian semigroup T(II) by giving an addition to the set of all equivalence classes in MII. The investigation of the semigroup T(II) seems interesting and important, because this gives a classification of the function fields of algebraic tori defined over a field k which split over a Galois extension of k with group II.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 56 , January 1975 , pp. 85 - 104
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1975

References

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