Results 1 to 10 of about 23,662 (137)
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
core +9 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
semanticscholar +3 more sources
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
semanticscholar +5 more sources
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
openaire +3 more sources
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 q-analogue of the wild fundamental group and the inverse problem of the Galois theory of q-difference equations [PDF]
, 2012 In previous papers, we defined $q$-analogues of alien derivations for linear analytic $q$-difference equations with integral slopes and proved a density theorem (in the Galois group) and a freeness theorem.
Ramis, Jean-Pierre, Sauloy, Jacques
core +3 more sources
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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Formalizing Galois Theory [PDF]
Experimental Mathematics, 2021 We describe a project to formalize Galois theory using the Lean theorem prover, which is part of a larger effort to formalize all of the standard undergraduate mathematics curriculum in Lean.
Thomas Browning, P. Lutz
semanticscholar +1 more source
The Fundamental Theorem of Finite Fields: A Proof from First Principles [PDF]
The American mathematical monthly, 2020 A mathematics student’s first introduction to the fundamental theorem of finite fields (FTFF) often occurs in an advanced abstract algebra course and invokes the power of Galois theory to prove it.
A. Chavez, C. O’Neill
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