Avsnittsöversikt
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In the first lecture we overview the course goals and we review some notion from abstract algebra
- Definition of field extension, degree of the field extension, field extension as vector space. The Galois group of a field extension.
- Rings of fractions, particularly the fraction field of an integral domain. See Section 7.5 of Dummit and Foote.
- Unique factorization domains (UFD) See Section 8.3 of Dummit and Foote.
- Gauss Lemma and Eisenstein criterion on factorization/irreducibility of polynomials. See Sections 9.3.-9.4 of Dummit and Foote.
Suggested Exercises:
DF Sec 9.4: 1, 2, 12
See exercise sheet