Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)


Nontrivial Galois module structure of cyclotomic fields

Authors: Marc Conrad and Daniel R. Replogle
Journal: Math. Comp. 72 (2003), 891-899
MSC (2000): Primary 11R33, 11R29; Secondary 11R27, 11R18
Published electronically: June 4, 2002
MathSciNet review: 1954973
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We say a tame Galois field extension $L/K$ with Galois group $G$ has trivial Galois module structure if the rings of integers have the property that $\mathcal{O}_{L}$ is a free $\mathcal{O}_{K}[G]$-module. The work of Greither, Replogle, Rubin, and Srivastav shows that for each algebraic number field other than the rational numbers there will exist infinitely many primes $l$ so that for each there is a tame Galois field extension of degree $l$ so that $L/K$ has nontrivial Galois module structure. However, the proof does not directly yield specific primes $l$ for a given algebraic number field $K.$ For $K$ any cyclotomic field we find an explicit $l$ so that there is a tame degree $l$extension $L/K$ with nontrivial Galois module structure.

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

Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2000): 11R33, 11R29, 11R27, 11R18

Retrieve articles in all journals with MSC (2000): 11R33, 11R29, 11R27, 11R18

Additional Information

Marc Conrad
Affiliation: Faculty of Technology, Southampton Institute, East Park Terrace, Southampton, S014 0YN Great Britain

Daniel R. Replogle
Affiliation: Department of Mathematics and Computer Science, College of Saint Elizabeth, 2 Convent Road, Morristown, New Jersey 07960

PII: S 0025-5718(02)01457-6
Keywords: Swan subgroups, cyclotomic units, Galois module structure, tame extension, normal integral basis
Received by editor(s): November 6, 2000
Received by editor(s) in revised form: July 15, 2001
Published electronically: June 4, 2002
Article copyright: © Copyright 2002 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia