The Structure of Arithmetic Fields

  • Dinakar Ramakrishnan
  • Robert J. Valenza
Part of the Graduate Texts in Mathematics book series (GTM, volume 186)


This chapter develops the basic structure theory for local and global fields; we follow A. Weil in stressing the topological rather than algebraic perspective, although perhaps less emphatically. Thus the more algebraically inclined will gain new insight into phenomena that have more often been treated in the context of the fraction field of a discrete valuation ring with finite residue field, or a Dedekind domain.


Prime Ideal Local Ring Topological Vector Space Prime Ring Residue Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Dinakar Ramakrishnan
    • 1
  • Robert J. Valenza
    • 2
  1. 1.Mathematics DepartmentCalifornia Institute of TechnologyPasadenaUSA
  2. 2.Department of MathematicsClaremont McKenna CollegeClaremontUSA

Personalised recommendations