Realizable Galois module classes for tetrahedral extensions
نویسندگان
چکیده
منابع مشابه
GALOIS MODULE STRUCTURE OF pTH-POWER CLASSES OF EXTENSIONS OF DEGREE p
For fields F of characteristic not p containing a primitive pth root of unity, we determine the Galois module structure of the group of pth-power classes of K for all cyclic extensions K/F of degree p. The foundation of the study of the maximal p-extensions of fields K containing a primitive pth root of unity is a group of the pth-power classes of the field: by Kummer theory this group describe...
متن کاملGALOIS MODULE STRUCTURE OF pTH-POWER CLASSES OF CYCLIC EXTENSIONS OF DEGREE p
In the mid-1960s Borevič and Faddeev initiated the study of the Galois module structure of groups of pth-power classes of cyclic extensions K/F of pth-power degree. They determined the structure of these modules in the case when F is a local field. In this paper we determine these Galois modules for all base fields F .
متن کاملGALOIS MODULE STRUCTURE OF GALOIS COHOMOLOGY FOR EMBEDDABLE CYCLIC EXTENSIONS OF DEGREE p
Let p > 2 be prime, and let n,m ∈ N be given. For cyclic extensions E/F of degree p that contain a primitive pth root of unity, we show that the associated Fp[Gal(E/F )]-modules H(GE , μp) have a sparse decomposition. When E/F is additionally a subextension of a cyclic, degree p extension E/F , we give a more refined Fp[Gal(E/F )]-decomposition of H (GE , μp).
متن کاملOn Certain Classes of Galois Extensions of Rings
Relations between the following classes of Galois extensions are given: (1) centrally projective Galois extensions (CP-Galois extensions), (2) faithfully Galois extensions, and (3) H-separable Galois extensions. Moreover, it is shown that the intersection of the class of CP-Galois extensions and the class of faithfully Galois extensions is the class of Azumaya Galois extensions.
متن کاملA pr 2 00 5 GALOIS MODULE STRUCTURE OF p TH - POWER CLASSES OF CYCLIC EXTENSIONS OF DEGREE
In the mid-1960s Borevič and Faddeev initiated the study of the Galois module structure of groups of pth-power classes of cyclic extensions K/F of pth-power degree. They determined the structure of these modules in the case when F is a local field. In this paper we determine these Galois modules for all base fields F . In 1947 Šafarevič initiated the study of Galois groups of maximal pextension...
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ژورنال
عنوان ژورنال: Compositio Mathematica
سال: 2005
ISSN: 0010-437X,1570-5846
DOI: 10.1112/s0010437x04001137