Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A note on Hilbert's Theorem 90


Authors: Bao-Ping Jia and Larry Santoni
Journal: Proc. Amer. Math. Soc. 118 (1993), 739-744
MSC: Primary 12F10; Secondary 11R27, 11R29, 11R32
DOI: https://doi.org/10.1090/S0002-9939-1993-1151813-9
MathSciNet review: 1151813
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we extend "up to powers" Hilbert's Theorem 90 to arbitrary finite Galois extensions. In the case of algebraic number fields with class number equal to $ 1$, we completely determine the kernel and image of the norm map.


References [Enhancements On Off] (What's this?)

  • [H] D. Hilbert, Theorie der Algebraische Zahlkorper, 1897, p. 147.
  • [J] Bao-Ping Jia, Splitting of rank-one valuations, Comm. Algebra 19 (1991), 777-794. MR 1102985 (92g:12009)
  • [K] Gregory Karpilovsky, Unit groups of classical rings, Oxford Science Publ., Clarendon Press, Oxford, 1988. MR 978631 (90e:20007)
  • [M] Daniel A. Marcus, Number fields, Springer-Verlag, New York, 1977. MR 0457396 (56:15601)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 12F10, 11R27, 11R29, 11R32

Retrieve articles in all journals with MSC: 12F10, 11R27, 11R29, 11R32


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1151813-9
Article copyright: © Copyright 1993 American Mathematical Society

American Mathematical Society