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A Stickelberger Condition on Cyclic Galois Extensions

Published online by Cambridge University Press:  20 November 2018

L. N. Childs
L. N. Childs*
Affiliation:
State University of New York at Albany, Albany, New York
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Let R be a commutative ring, C a finite abelian group, S a Galois extension of R with group C, in the sense of [1]. Viewing S as an RC-module defines the Picard invariant map [4] from the Harrison group Gal (R, C) of isomorphism classes of Galois extensions of R with group C to CI (RC), the class group of RC. The image of the Picard invariant map is known to be contained in the subgroup h Cl (RC) of primitive elements of CI (RC) (for definition see below). Characterizing the image of the Picard invariant map has been of some interest, for the image describes the extent of failure of Galois extensions to have normal bases.

Let R be the ring of integers of an algebraic number field K.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 34 , Issue 3 , 01 June 1982 , pp. 686 - 690
Copyright
Copyright © Canadian Mathematical Society 1982

References

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