scholarly journals The Fundamental Theorem on Symmetric Polynomials: History's First Whiff of Galois Theory

2017 ◽  
Vol 48 (1) ◽  
pp. 18-29 ◽  
Author(s):  
Ben Blum-Smith ◽  
Samuel Coskey
Keyword(s):  
Fundamental Theorem ◽  
Galois Theory ◽  
Symmetric Polynomials

Another Proof of the Fundamental Theorem of Galois Theory

1968 ◽  
Vol 75 (7) ◽  
pp. 720
Author(s):  
Frank DeMeyer
Keyword(s):  
Fundamental Theorem ◽  
Galois Theory

scholarly journals Galois Theory with Infinitely Many Idempotents

1969 ◽  
Vol 35 ◽  
pp. 83-98 ◽  
Author(s):  
O.E. Villamayor ◽  
D. Zelinsky
Keyword(s):  
Finite Group ◽  
Fundamental Theorem ◽  
Galois Theory ◽  
Linear Independence ◽  
Commutative Rings ◽  
Classical Field ◽  
Fixed Field ◽  
Noncommutative Rings ◽  
Real Change ◽  
A Finite Group

In 1942 Artin proved the linear independence, over a field S, of distinct automorphism of S; in other words if G is a finite group of automorphisms of S and R is the fixed field, then Horn^S, S) is a free S-module with G as basis. Since then, this last condition (“S is G-Galois”) or its equivalents have been used as a postulate in all the Galois theories of rings that are not fields, for example by Dieudonné, Jacobson, Azumaya and Nakayama for noncommutative rings and then in [AG, Appendix] and [CUR] for commutative rings. When S has no idempotents but 0 and 1, [CHR] proves that the ordinary fundamental theorem of Galois theory holds with no real change from the classical, field case.

THE FUNDAMENTAL THEOREM OF GALOIS THEORY

1989 ◽  
Vol 64 (2) ◽  
pp. 359-374 ◽  
Author(s):  
G Z Dzhanelidze
Keyword(s):  
Fundamental Theorem ◽  
Galois Theory
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