Results 31 to 40 of about 48,689 (198)
Separable subalgebras of a class of Azumaya algebras
International Journal of Mathematics and Mathematical Sciences, 1998 Let S be a ring with 1, C the center of S, G a finite automorphism group of S of order n invertible in S, and SG the subnng of elements of S fixed under each element in G. It is shown that the skew group ring S*G is a G′-Galois extension of (S*G)G′ that
George Szeto
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On Galois Conditions and Galois Groups of Simple Rings [PDF]
Transactions of the American Mathematical Society, 1965 Throughout the present paper, R will be a simple ring, where we shall understand by a simple ring a total matrix ring over a division rings. If S' is any subring containing the identity element 1 of R, we denote by VR(S') the centralizer of S' in R, VR(S') = VR(VR(S')) and by 0 (S', R) we denote the group of all automorphisms of R which are the ...
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Transactions of the London Mathematical Society, 2019 Recently, there has been much interest in studying the torsion subgroups of elliptic curves base‐extended to infinite extensions of Q. In this paper, given a finite group G, we study what happens with the torsion of an elliptic curve E over Q when ...
Harris B. Daniels +2 more
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From Galois to Hopf Galois: theory and practice
, 2014 Hopf Galois theory expands the classical Galois theory by considering the Galois property in terms of the action of the group algebra k[G] on K/k and then replacing it by the action of a Hopf algebra.
Crespo, Teresa +2 more
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On Galois cohomology and realizability of 2-groups as Galois groups II
Open Mathematics, 2011 Abstract In [Michailov I.M., On Galois cohomology and realizability of 2-groups as Galois groups, Cent. Eur. J. Math., 2011, 9(2), 403–419] we calculated the obstructions to the realizability as Galois groups of 14 non-abelian groups of order 2n, n ≥ 4, having a cyclic subgroup of order 2n−2, over fields containing a primitive 2n−3th ...
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Construction and Characterization of Galois Algebras with Given Galois Group [PDF]
Nagoya Mathematical Journal, 1950 Recently H. Hasse has given an interesting theory of Galois algebras, which generalizes the well known theory of Kummer fields; an algebra over a field Ω is called a Galois algebra with Galois group G when possesses G as a group of automorphisms and is (G, Ω)-operator-isomorphic to the group ring G(Ω) of G over Ω. On assuming that the characteristic
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Symplectic Groups as Galois Groups
Journal of Algebra, 2000 Let \(\mathbb{F}\) be a field containing the field of order \(q\), let \(x\) and \(t\) be indeterminates, let \(m\) be an integer greater than 1, and let \[ \widehat{f}(Y)= Y^{q^{2m}}+ t^q Y^{q^{m+1}}+ xY^{q^m}+ tY^{q^{m-1}}+Y. \] In [\textit{S. S. Abhyankar}, Proc. Am. Math. Soc. 124, 2977--2991 (1996; Zbl 0866.12005)], it was shown that, for \(m>2\),
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Coincidence of two Swan conductors of abelian characters [PDF]
Épijournal de Géométrie Algébrique, 2019 There are two ways to define the Swan conductor of an abelian character of the absolute Galois group of a complete discrete valuation field. We prove that these two Swan conductors coincide.
Kazuya Kato, Takeshi Saito
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On the additive image of zeroth persistent homology
Transactions of the London Mathematical Society, Volume 13, Issue 1, December 2026.Abstract For a category X$X$ and a finite field F$F$, we study the additive image of the functor H0(−;F)∗:rep(X,Top)→rep(X,VectF)$\operatorname{H}_0(-;F)_* \colon \operatorname{rep}(X, \mathbf {Top}) \rightarrow \operatorname{rep}(X, \mathbf {Vect}_F)$, or equivalently, of the free functor rep(X,Set)→rep(X,VectF)$\operatorname{rep}(X, \mathbf {Set ...
Ulrich Bauer +3 more
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New Arcs in PG(3,8) by Singer Group
Al-Mustansiriyah Journal of Science, 2022 In this paper, studied the types of (k, r)-arcs were constructed by action of groups on the three-dimensional projective space over the Galois field of order eight. Also, determined if they form complete arcs or not.
Najm Abdulzahra Al-seraji +2 more
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