Abstract
By an algebraic number-field, it is customary to understand a finite algebraic extension of Q. One main object of this book, and of number-theory in general, is to study algebraic number-fields by means of their embeddings into local fields. In the last century, however, it was discovered that the methods by which this can be done may be applied with very little change to certain fields of characteristic p >1; and the simultaneous study of these two types of fields throws much additional light on both of them. With this in mind, we introduce as follows the fields which will be considered from now on:
Definition 1. A field will be called an A -field if it is either a finite algebraic extension of Q or a finitely generated extension of a finite prime field F p , of degree of transcendency 1 over F p .
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1973 Springer Science+Business Media New York
About this chapter
Cite this chapter
Weil, A. (1973). Places of A-fields. In: Basic Number Theory. Die Grundlehren der mathematischen Wissenschaften, vol 144. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05978-4_3
Download citation
DOI: https://doi.org/10.1007/978-3-662-05978-4_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-05980-7
Online ISBN: 978-3-662-05978-4
eBook Packages: Springer Book Archive