Abstract Algebra I (Groups, Rings, and Vector Spaces III): Topics list

Topics & Pacing

The following is a rough list of arguments covered in class.

Sep 17

Normal and splitting fields: Definitions and examples.

Sep 14

Proof that the fields of constructible numbers are extensions of Q of degree a power of 2; some geometric impossibilities.

Sep 12

Constructions with straightedge and compass: constructible elements in R and C.

Sep 10

Proof of the Nullstellensatz.

Sep 7

Maximal ideals in k[x₁,...,x_n]. Affine space. Algebraic sets, Zariski topology. Radical ideals.

Sep 5

Uniqueness of the algebraic closure. Nullstellensatz: For a field k finite type implies finite.

Aug 31

Artin's construction of the algebraic closure of a field.

Aug 19

Review of Field Extensions (sect. VII. 1) and computations of simple extensions.

Aug 27

Review of Field Extensions (sect. VII. 1)