Splitting algebras, Symmetric functions and Galois Theory

2002/11/06 by Torsten Ekedahl, Dan Laksov, Ekedahl, Torsten +1
Computer Science · Mathematics · #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #Polynomial and algebraic computation #math.AC #msc:12F05 #msc:12F10 #msc:13A50 #msc:13B25

paper · pdf · doi:10.48550/arxiv.math/0211125

13 pages

arxiv created 2002/11/06 · arxiv updated 2009/11/30

Abstract

We present a theory for splitting algebras of monic polynomials over rings, and apply the results to symmetric functions, and Galois theory. Our main result is that the ring of invariants of a splitting algebra under the symmetric group almost always is the ring of coefficients.

Related

• On the invariants of the splitting algebra
• A necessary and sufficient condition for the existence of non-trivial S_n-invariants in the splitting algebra
• Generalized symmetric functions
• On the splitting ring of a polynomial
• Takiff algebras with polynomial rings of symmetric invariants