No Galois Theory in Godement's Cours d'Algebre?

Question

I just procured an English translation of Godement's Cours d'Algebre and was interested in reading the treatment of Galois Theory. I started to look for the relevant chapter in the ToC, but to my surprise the name "Galois" was nowhere to be found. Then I checked the index and it couldnt be found there either. But the author claims that his book covers the whole undergraduate algebra curriculum for UK universities, and this definitely includes Galois Theory, so I'm slightly confused. Does this have anything to do with politics? Any explanation/clarification would be much appreciated!

Answer 1

There are four references to Galois in the (English translation) of the book :

• page 13 : general intro to Groups, rings, fields

• page 121 : Historically, it was the study of these groups (when the set $X$ is finite) by Galois that led to the general and "abstract" notion of a group.

• page 154 : The first detailed study of finite fields was made by Galois.

• pages 198 (footnote) : The study of algebraic numbers in the 19th century, by Galois and by the great mathematicians of the German school (Gauss, Kummer, Jacobi, Lejeune-Dirichlet, Dedekind, Kronecker, Hilbert), is at the origin of all of modern algebra and leads to results which are undoubtedly the deepest in the whole of mathematics.

and three more in the Bibliography.

As you said, there is no entry for Galois in the Index of Terminology, that is not an Index of Name.

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We can see that also Nicolas Bourbaki, Elements of Mathematics. Algebra I: Chapters 1-3 (1998 - French ed.1970) has many references to Galois but treats Ordered groups and fields and not "Galois theory".

Answer 2

The extraordinary book "Cours d'Algèbre", de Godement was written in French because the conjuncture, in 1966, "a rendu urgente la redaction, en français, d'un ouvrage de référence accesible aux débutants"........"on a donc fait en sorte que sa lecture ne demande pas d'autres connaissances que celles qu'on pourrait acquérir dans l"Enseignement Secondaire”.

I never forget the great impression made me the end of the book: "In a triangle, the length of each side is less than the sum of the lengths of the other two sides" .... but in the context of Hermitian forms, i.e. on Hilbert spaces but without naming them (although Hilbert is appointed, for the celebrate “Nullstellensatz” on the part of algebraically closed fields).

Is not uncommon for translation of a book, it has some variations or adaptations; I do not know the translation matter of this post but the original work in French has been always for me as a work of art.