Results 1 to 10 of about 23,158 (121)
The Fundamental Theorem on Symmetric Polynomials: History's First Whiff of Galois Theory [PDF]
The College Mathematics Journal, 2017 16 pages, 1 figure.
Blum-Smith, Ben, Coskey, Samuel
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A simple proof of the fundamental theorem of Galois theory [PDF]
, 2022 We give a simple proof of the fundamental theorem of Galois theory which provides a correspondence between the intermediate fields of a finite Galois extension and the subgroups of its Galois group. The proof relies on the combinatorial fact that a field cannot be written as a union of finitely many proper subfields.
Martin Brandenburg
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An adaptive cryptosystem on a Finite Field [PDF]
PeerJ Computer Science, 2021 Owing to mathematical theory and computational power evolution, modern cryptosystems demand ingenious trapdoor functions as their foundation to extend the gap between an enthusiastic interceptor and sensitive information.
Awnon Bhowmik, Unnikrishnan Menon
doaj +3 more sources
The Fundamental Theorem of Algebra (with Galois Theory)
, 2012 This post assumes familiarity with some basic concepts in abstract algebra, specifically the terminology of field extensions, and the classical results in Galois theory and group theory. The fundamental theorem of algebra has quite a few number of proofs (enough to fill a book!).
Jeremy Kun
+4 more sources
The Fundamental Theorem of Galois Theory (pdf)
, 2013 We give a short and self-contained proof of the Fundamental Theorem of Galois Theory. (This a pdf file. Tex file: link below.)
Pierre-Yves Gaillard
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On the fundamental theorem of the Galois theory for finite factors [PDF]
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1960 Nakamura, Masahiro, Takeda, Zirô
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Four-Fold Formal Concept Analysis Based on Complete Idempotent Semifields
Mathematics, 2021 Formal Concept Analysis (FCA) is a well-known supervised boolean data-mining technique rooted in Lattice and Order Theory, that has several extensions to, e.g., fuzzy and idempotent semirings.
Francisco José Valverde-Albacete +1 more
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Galois theory of fuchsian q-difference equations [PDF]
, 2002 We propose an analytical approach to the Galois theory of singular regular linear q-difference systems. We use Tannaka duality along with Birkhoff's classification scheme with the connection matrix to define and describe their Galois groups.
Sauloy, Jacques
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Fundamental groups of topological stacks with slice property [PDF]
, 2007 The main result of the paper is a formula for the fundamental group of the coarse moduli space of a topological stack. As an application, we find simple general formulas for the fundamental group of the coarse quotient of a group action on a topological ...
Armstrong +8 more
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The Galois group of a stable homotopy theory [PDF]
, 2016 To a "stable homotopy theory" (a presentable, symmetric monoidal stable $\infty$-category), we naturally associate a category of finite \'etale algebra objects and, using Grothendieck's categorical machine, a profinite group that we call the Galois group.
Mathew, Akhil
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