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didn't mean that all field theory is now Galois theory, but that Galois theory became a branch of field theory, unlike in Galois' original formulation. For...

on Galois extensions. On Galois groups, reorganised a bit, included link back to Galois theory for "more elementary examples". Updated the "Galois theory"...

differential field extension and differential Galois theory should be separate articles (compare Galois theory vs. algebraic extension (or equivalently with...

all the Galois theory pages. I am planning to put up a summary plus ideas for future work in the next few hours, probably on the Galois theory discussion...

also says In the case of a Galois extension L/K the subgroup of all automorphisms of L fixing K pointwise is called the Galois group of the extension. So...

The notion of resolvent is a well established notion in Galois theory. The readers of WP looking for them need to be informed that they exist, despite...

understand what a Group is, and what a Galois Group is for that matter. I am curious about this mysterious Absolute Galois Group (having read about it elsewhere)...

groups have been introduced a long time before blocks and are basic for Galois theory. If a merger make sense, it would be to merge this article into Primitive...

Need to add the definition (and properties?) of Galois insertions, that is Galois connections with a composition of adjoins being the identity function...

There is a differential Galois theory, but it was developed by others, such as Picard and Vessiot, and it provides a theory of quadratures, the indefinite...

explain the importance of the theory of separable extensions. The theory of separable extensions is important in Galois theory and this is well established...

group action) leads to the elementary Galois duality in (the trivial part of) Galois theory. In general, concept theory can be useful in order to clearly...

and all finite fields. This criterion is of technical importance in Galois theory. In this connection, the concept of separability is of lesser importance...

describes them together, and are both about using endomorphism rings for a Galois theory of algebras. The density theorem has wider applications, so is covered...

the reviewers decided that Galois' submissions lacked sufficient detail and told him to revise and resubmit them. So Galois apparently withdrew the two...

from Calabi. This error also appears in ex. 1.12 of the latest edition of Galois Theory by Ian Stewart Bertbeerpot (talk) 23:11, 29 January 2023 (UTC)...

suffice. Alternatively, a stronger statement that is useful in setting up Galois theory is that f can be expressed ... if and only if f can be expressed as...

though the statements were stated and proved in Emil Artin's book "Galois Theory" from 1942, what is here called Artin's theorem should be rather called...

of Galois which finally showed that there are quintics which are not solvable, since a polynomial is solvable by radicals if and only if it's Galois group...

2010 (UTC) Galois is said to have been a Catholic in the box in the article. Both his parents were anti-Catholic and I am not sure that Galois was baptised...