Results 1 to 10 of about 40,312 (218)
The Galois algebras and the Azumay Galois extensions [PDF]
International Journal of Mathematics and Mathematical Sciences, 2002 Let B be a Galois algebra over a commutative ring R with Galois group G, C the center of B, K={g∈G|g(c)=c for all c∈C}, Jg{b∈B|bx=g(x)b for all x∈B} for each g∈K, and BK=(⊕∑g∈K Jg). Then BK is a central weakly Galois algebra with Galois group induced by
George Szeto, Lianyong Xue
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Hopf Differential Graded Galois Extensions [PDF]
Mathematics, 2022 We introduce the concept of Hopf dg Galois extensions. For a finite dimensional semisimple Hopf algebra H and an H-module dg algebra R, we show that D(R#H)≅D(RH) is equivalent to that R/RH is a Hopf differential graded Galois extension.
Bo-Ye Zhang
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Parametric Galois extensions [PDF]
Journal of Algebra, 2014 Given a field $k$ and a finite group $H$, {\it{an $H$-parametric extension over $k$}} is a finite Galois extension of $k(T)$ of Galois group containing $H$ which is regular over $k$ and has all the Galois extensions of $k$ of group $H$ among its specializations.
François Legrand
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On Hopf Galois Hirata extensions [PDF]
International Journal of Mathematics and Mathematical Sciences, 2003 Let H be a finite-dimensional Hopf algebra over a field K, H* the dual Hopf algebra of H, and B a right H*-Galois and Hirata separable extension of BH. Then B is characterized in terms of the commutator subring VB(BH) of BH in B and the smash product VB ...
George Szeto, Lianyong Xue
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On Generalized Hopf Galois Extensions [PDF]
Journal of Pure and Applied Algebra, 2004 23 ...
Peter Schauenburg, Henriette Schneider
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Derived equivalence, recollements under H-Galois extensions
AIMS Mathematics, 2023 In this paper, assume that $ H $ is a Hopf algebra and $ A/B $ is an $ H $-Galois extension. Firstly, by introducing the concept of an $ H $-stable tilting complex $ T_{\bullet} $ over $ B $, we show that $ T_{\bullet}\otimes_BA $ is a tilting complex ...
Jinlei Dong, Fang Li, Longgang Sun
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Gorenstein Flat Modules of Hopf-Galois Extensions
Mathematics, 2023 Let A/B be a right H-Galois extension over a semisimple Hopf algebra H. The purpose of this paper is to give the relationship of Gorenstein flat dimensions between the algebra A and its subalgebra B, and obtain that the global Gorenstein flat dimension ...
Qiaoling Guo +3 more
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Nontrivial Galois module structure of cyclotomic fields [PDF]
, 2002 We say a tame Galois field extension $L/K$ with Galois group $G$ has trivial Galois module structure if the rings of integers have the property that $\Cal{O}_{L}$ is a free $\Cal{O}_{K}[G]$-module.
Conrad, Marc, Replogle, Daniel R.
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Generic Galois extensions [PDF]
Proceedings of the National Academy of Sciences, 1980 We define the notion of a generic Galois extension with group G over a field F . Let R be a communtative ring of the form F [ x 1 ,..., x n ](1/
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Cyclic Homology and Quantum Orbits [PDF]
, 2015 A natural isomorphism between the cyclic object computing the relative cyclic homology of a homogeneous quotient-coalgebra-Galois extension, and the cyclic object computing the cyclic homology of a Galois coalgebra with SAYD coefficients is presented ...
Maszczyk, Tomasz, Sütlü, Serkan
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