- Definition of rings, group of units, integral domains, fields.
- Polynomial rings, homomorphisms, ideals, quotients, division algorithm.
- Factorization in domains, Euclidean Domain, Unique Factorization Domain, Principal Ideal Domain.
- Integral extensions, primes in integral extensions.
- Field extensions, algebraic extensions, degree of an extension.
- Splitting fields, normal extensions, separable extensions.
- Galois Theory: Galois extensions, automorphism groups and fixed fields, fundamental theorem of Galois theory and applications, cyclic extensions, cyclotomic polynomials, solvability by radicals, constructibility of regular polygons.
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