Galois extension
On characterizations of a center Galois extension
... commutative Galois extension C is characterized in terms of the ideals generated by {c −g(c) | c ∈ C} for g ≠ 1 in G, that is C is a Galois extension with Galois group G if and only if ...
6
On Azumaya Galois extensions and skew group rings
... Azumaya Galois extension of a ring are given in terms of the Azumaya skew group ring of the Galois group over the extension and a Galois extension of a ring with a special ...
5
The Galois algebras and the Azumay Galois extensions
... a Galois algebra over a com- mutative ring R with Galois group G, C the center of B, and K = { g ∈ G | g(c) = c for all c ∈ C } ...a Galois extension, a Galois algebra, a cen- tral ...
6
On certain classes of Galois extensions of rings
... H-separable Galois extensions. In [9], the class of H-separable G-Galois exten- sion was ...CP-Galois extension, and an H-separable and a faithfully Galois ...
7
The Boolean algebra of Galois algebras
... 2. Definitions and notations. Let B be a ring with 1, C the center of B, G an automorphism group of B of order n for some integer n, and B G the set of elements in B, fixed under each element in G. B is called a ...
7
Hofer, Martin Gerhard (2018): Elliptic p-units and the equivariant Tamagawa Number Conjecture. Dissertation, LMU München: Fakultät für Mathematik, Informatik und Statistik
... a Galois-equivariant conjectural link between the values at s = 0 of the first non-vanishing derivative of the S-imprimitive Artin L-function L K/k,S (s, χ) associated to a Galois extension of number ...
163
The Galois extensions induced by idempotents in a Galois algebra
... The extension B is a Galois extension with Galois group G(e) for a central idempotent e of B if and only if B = Be ⊕ B(1− e) such that Be and B(1− e) are Galois extensions with ...
6
On partial Galois Azumaya extensions
... of Galois Azumaya extension was introduced by Alfaro and Szeto in [3], motivated by an early work by themselves [2] about the conditions necessary and sufficient for a skew group ring to be ...algebra, ...
14
Galois 2-Extensions
... Q / Z ) be the Pontrjagin dual of V. Then V ∗ is a profinite (abelian) group. By [Wat74, Theorem 2] there exists a field F of characteristic p such that F admits a Galois extension L/F with Gal(L/F) = V ∗ . ...
105
On the Galois structure of Selmer groups
... Abstract. Let A be an abelian variety defined over a number field k and F a finite Galois extension of k. Let p be a prime number. Then under certain not-too-stringent conditions on A and F we investigate ...
17
On separable group rings
... Moreover, Galois extensions of a ring satisfying the fundamental theorem were studied in ...the Galois map for a non-Galois extension RG of (RG) G ...
8
On central commutator Galois extensions of rings
... commutator Galois extensions is ...Azumaya Galois extensions and Galois H-separable ...commutator Galois extension are ...commutator Galois extension of B G if and only if ...
6
Ramification In The Inverse Galois Problem
... inverse Galois problem. We explore what finite groups appear as the Galois group of an extension of the rational numbers in which only a predetermined set of primes may ...the Galois group of ...
84
GENERIC GALOIS EXTENSIONS FOR FAMILIES OF FINITE GROUPS
... for any finite group G and any field k, there does not always exist a generic Galois extension for G over k. However, we have shown that there always exists a G-Galois extension S'/R' [r] ...
79
Computational aspects of Galois representations
... integral Galois representations; this is due to the fact that for two different integral Galois representations coming from two different stable lattices, we may not have that they are equivalent as ...
92
Discrete Logarithm in Galois Rings
... use Galois rings to perform ElGamal encryption through the concept of the discrete logarithm and the ...in Galois rings GR(p k , m) allows to express each element α ∈ GR(p k , m) in the form: α = ξ (x 0 ,x ...
12
Special Frobenius Traces in Galois Representations
... The study of Galois representations coming from arithmetic geometry is of primary importance in modern number theory. In particular, the traces of the images of the Frobenius elements under these representations ...
65
Normal Bases on Galois Ring Extensions
... Keywords: Galois ring; optimal normal basis; multiplicative complexity; finite field4. Introduction 65[r] ...
14
Certification of modular Galois representations
... data. As we reran the computations with the certified resolvents, we realised that [Pari/GP] can do the same thing in less than 1 minute. The reason for this is that [SAGE] takes the time to check rigorously that p is ...
46
On separable abelian extensions of rings
... Abelian ring extensions, separable algebras, Azumaya.. algebras, Galois extensions..[r] ...
6