Galois' way of talking about this process was to elaborate and somewhat alter the meaning of the word "rational." Galois explained that "rational" in his work would mean a quantity expressible …

Sep 21, 2017 · I'm currently trying to read the six page proof Galois theory for beginners but it's proving to be harder than I thought. The author seems to expect the reader to make some …

Mar 25, 2016 · As we all know Galois is an ultimate math prodigy. At age 17 or 18 he published a paper which we now know as Galois theory. I want to just see how he thought mathematics by …

Jul 31, 2023 · Galois theory has always struck me as rather mysterious, perhaps because its modern formulation is shrouded in concepts that did not yet exist during Galois' time (e.g., …

May 21, 2021 · The Galois correspondence is profound in number theory because it leads to a highly nonobvious way of turning prime ideals into field automorphisms (this uses Galois …

Nov 16, 2011 · Is there an analogous theory to Galois extension of fields for commutative rings? In particular, what does it mean for a ring extension to be Galois? Thanks.

Dec 1, 2014 · However, the Galois group is an uncountable profinite group, and so to give any short description in terms of generators and relations leads you into subtle issues about which …

Any thoughts on David Cox's Galois Theory vs. Lang Undergraduate Algebra vs. Weintraub for an introduction to Galois Theory with aims to progress as Galois Theory -> Algebraic Number …

Oct 20, 2011 · A Galois field is a finite field (from the Wikipedia article): In abstract algebra, a finite field or Galois field (so named in honor of Évariste Galois) is a field that contains a finite …

May 14, 2010 · Hi. Are there nice/simple examples of cyclic extensions $L/K$ (that is, Galois extensions with cyclic Galois group) for which $L$ cannot be written as $K(a)$ with $a ...