Avsnittsöversikt
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We start put down the basis needed to understand and prove the fundamental theorem of Galois theory . The main goal of today is to give a charracterization of finite extension. to do that we need to cover the following topics
- Algebraic and trascendental extension
- Simple extension and finitely generated extension
- minimal polynomial of an algebraic element, degree of the corresponding simple field extension
- degrees of towers of field extenstion
- finite extension is equivalent to algebraic and finitely generated
References for Topic 1: (a) Dummit and Foote: 13.1-13.2
Suggested exercises
DF Section 13.1: 1, 2, 3
DF Section 13.2: 1, 3,7, 10, 13