Hostname: page-component-7b7567c8c-2n9c9 Total loading time: 0 Render date: 2026-11-15T22:52:38.652Z Has data issue: false hasContentIssue false
  • English
  • Français

Ramification Theory for Extensions of Degree p

Published online by Cambridge University Press:  22 January 2016

Susan Williamson
Susan Williamson*
Affiliation:
Regis College, Weston, Massachusetts
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

The notions of tame and wild ramification lead us to make the following definition.

Definition. The quotient field extension of an extension of discrete rank one valuation rings is said to be fiercely ramified if the residue class field extension has a nontrivial inseparable part.

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 41 , February 1971, pp. 149 - 168
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1971

References

[1] Artin, E. and Tate, J., Class field theory, Benjamin, (1967).Google Scholar
[2] Auslander, M. and Buchsbaum, D., On ramification theory in noetherian rings, Amer. J. of Math. Vol. 81 (1959), pp. 749–765.Google Scholar
[3] Cassels, J.W.S. and Frolich, A., Algebraic Number Theory, Thompson, (1967).Google Scholar
[4] Nagata, M., Local Rings, Wiley, (1962).Google Scholar
[5] Serre, J.P., Corps Locaux, Paris, Hermann, (1962).Google Scholar
[6] Weiss, E., Algebraic Number Theory, McGraw-Hill, (1963).Google Scholar
[7] Williamson, S., Equivalence classes of maximal orders, Nagoya Math. J. Vol. 31 (1968), pp. 131–171.Google Scholar
[8] Zariski, O. and Samuel, P., Commutative Algebra, Vol. 1, Van Nostrand, (1958).Google Scholar