Abstract
In the last chapter we discussed the general theory of algebraic number fields and their rings of integers. We now consider in greater detail two important classes of these fields which were studied first in the nineteenth century by Gauss, Eisenstein, Kummer, Dirichlet, and others in connection with the theory of quadratic forms, higher reciprocity laws and Fermâtes Last Theorem. The reader who is interested in the historical development of this subject should consult the book by H. Edwards [128] as well as the classical treatise by H. Smith [72].
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1990 Springer Science+Business Media New York
About this chapter
Cite this chapter
Ireland, K., Rosen, M. (1990). Quadratic and Cyclotomic Fields. In: A Classical Introduction to Modern Number Theory. Graduate Texts in Mathematics, vol 84. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2103-4_13
Download citation
DOI: https://doi.org/10.1007/978-1-4757-2103-4_13
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3094-1
Online ISBN: 978-1-4757-2103-4
eBook Packages: Springer Book Archive