On the Galois module structure of cyclic Kummer extensions
نویسندگان
چکیده
منابع مشابه
GALOIS 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 کاملHopf Galois structures on Kummer extensions of prime power degree
Let K be a field of characteristic not p (an odd prime), containing a primitive p-th root of unity ζ, and let L = K[z] with x n − a the minimal polynomial of z over K: thus L|K is a Kummer extension, with cyclic Galois group G = 〈σ〉 acting on L via σ(z) = ζz. T. Kohl, 1998, showed that L|K has pn−1 Hopf Galois structures. In this paper we describe these Hopf Galois structures.
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 کاملthe structure of lie derivations on c*-algebras
نشان می دهیم که هر اشتقاق لی روی یک c^*-جبر به شکل استاندارد است، یعنی می تواند به طور یکتا به مجموع یک اشتقاق لی و یک اثر مرکز مقدار تجزیه شود. کلمات کلیدی: اشتقاق، اشتقاق لی، c^*-جبر.
15 صفحه اولGalois Module Structure of Galois Cohomology
Let F be a field containing a primitive pth root of unity, and let U be an open normal subgroup of index p of the absolute Galois group GF of F . We determine the structure of the cohomology group H(U, Fp) as an Fp[GF /U ]-module for all n ∈ N. Previously this structure was known only for n = 1, and until recently the structure even of H(U, Fp) was determined only for F a local field, a case se...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2008
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2008.06.034