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Carlitz Modules and Normal Integral Bases

โœ Scribed by Chapman, R. J.

Book ID
120094784
Publisher
Oxford University Press
Year
1991
Tongue
English
Weight
237 KB
Volume
s2-44
Category
Article
ISSN
0024-6107

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Let L#F be cyclotomic function fields of Carlitz. We show that if Lร‚F is Carlitz Kummer, the integer ring O L is free over the associated order as in the classical cyclotomic Kummer extension. However, contrary to the characteristic zero case, O L is not free unless Lร‚F is Carlitz Kummer.