English

Galois Theory without abstract algebra

History and Overview 2011-08-24 v1

Abstract

Galois theory is developed using elementary polynomial and group algebra. The method follows closely the original prescription of Galois, and has the benefit of making the theory accessible to a wide audience. The theory is illustrated by a solution in radicals of lower degree polynomials, and the standard result of the insolubility in radicals of the general quintic and above. This is augmented by the presentation of a general solution in radicals for all polynomials when such exist, and illustrated with specific cases. A method for computing the Galois group and establishing whether a radical solution exists is also presented.

Keywords

Cite

@article{arxiv.1108.4593,
  title  = {Galois Theory without abstract algebra},
  author = {Leonid Lerner},
  journal= {arXiv preprint arXiv:1108.4593},
  year   = {2011}
}
R2 v1 2026-06-21T18:54:09.037Z