Scope of chapter 8

[ghost]

The current list of sections of chapter 8 in the Symmetry Book on fields is as follows:

1. the algebraic hierarchy: groups, abelian groups, rings, fields
2. vector spaces
3. the general linear group as automorphism group
4. determinants
5. examples: rationals, polynomials, adding a root, field extensions
6. ordered fields, real-closed fields, pythagorean fields, euclidean fields
7. complex fields, quadratically closed fields, algebraically closed fields

In addition, there is this list of other topics at the beginning of the chapter:
Quotients; subspaces (= ?). Bases and so. Dual space; orthogonality. (all of this depends on good implementations of subobjects). Eigen-stuff. Characteristic polynomials; Hamilton-Cayley.

However, in #140 (comment) Ulrik Buchholtz implied that covering this many topics is no longer appropriate for this book, and that the scope of this chapter would need to be narrowed down. Which topics in the list above should be kept, and which topics should be removed from the list?

[DanGrayson]

I would say that pythagorean fields, euclidean fields, and quadratically closed fields need not be taught. The rest is standard in undergraduate algebra courses.