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Some interactions between Hopf Galois extensions and noncommutative rings
Universitas Scientiarum, 2022 In this paper, our objects of interest are Hopf Galois extensions (e.g., Hopf algebras, Galois field extensions, strongly graded algebras, crossed products, principal bundles, etc.) and families of noncommutative rings (e.g., skew polynomial rings, PBW ...
Armando Reyes, Fabio Calderón
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Hopf Differential Graded Galois Extensions
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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Polynomial composites and certain types of fields extensions
Karpatsʹkì Matematičnì Publìkacìï, 2023 In this paper, we consider polynomial composites with the coefficients from $K\subset L$. We already know many properties, but we do not know the answer to the question of whether there is a relationship between composites and field extensions.
Ł. Matysiak
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Some Implicational Semilinear Gaggle Logics: (Dual) Residuated-Connected Logics
Axioms, 2022 Implicational partial Galois logics and some of their semilinear extensions, such as semilinear extensions satisfying abstract Galois and dual Galois connection properties, have been introduced together with their relational semantics.
Eunsuk Yang
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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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Global Solvably Closed Anabelian Geometry [PDF]
, 2006 In this paper, we study the pro-Σ anabelian geometry of hyperbolic curves, where Σ is a nonempty set of prime numbers, over Galois groups of “solvably closed extensions” of number fields — i.e., infinite extensions of number fields which have ...
Mochizuki, Shinichi
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Homotopy theory of Hopf Galois extensions [PDF]
, 2004 We introduce the concept of homotopy equivalence for Hopf Galois extensions and make a systematic study of it. As an application we determine all H-Galois extensions up to homotopy equivalence in the case when H is a Drinfeld-Jimbo quantum group.Comment:
Kassel, Christian +1 more
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On certain classes of Galois extensions of rings
International Journal of Mathematics and Mathematical Sciences, 2001 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.
George Szeto, Lianyong Xue
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Infinite Towers of Galois Defect Extensions of Kaplansky Fields
Annales Mathematicae Silesianae, 2018 We give conditions for Kaplansky fields to admit infinite towers of Galois defect extensions of prime degree. As proofs of the presented facts are constructive, this provides examples of constructions of infinite towers of Galois defect extensions of ...
Blaszczok Anna
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Hopf Quasigroup Galois Extensions and a Morita Equivalence
Mathematics, 2023 For H, a Hopf coquasigroup, and A, a left quasi-H-module algebra, we show that the smash product A#H is linked to the algebra of H invariants AH by a Morita context.
Huaiwen Guo, Shuanhong Wang
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