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0.1
Notation.
0.1
Notation.
0.2
References.
1
Basic Definitions and Results
1.1
Rings
1.2
Fields
1.3
The characteristic of a field
1.4
Review of polynomial rings
1.5
Factoring polynomials
1.6
Extensions
1.7
The subring generated by a subset
1.8
The subfield generated by a subset
1.9
Construction of some extensions
1.10
Stem fields
1.11
Algebraic and transcendental elements
1.12
Transcendental numbers
1.13
Constructions with straight-edge and compass.
1.14
Algebraically closed fields
1.15
Exercises
2
Splitting Fields; Multiple Roots
3
The Fundamental Theorem of Galois Theory
Chapter 1
Basic Definitions and Results
1.1
Rings
1.2
Fields
1.3
The characteristic of a field
1.4
Review of polynomial rings
1.5
Factoring polynomials
1.6
Extensions
1.7
The subring generated by a subset
1.8
The subfield generated by a subset
1.9
Construction of some extensions
1.10
Stem fields
1.11
Algebraic and transcendental elements
1.12
Transcendental numbers
1.13
Constructions with straight-edge and compass.
1.14
Algebraically closed fields
1.15
Exercises