742 - Abstract Algebra II

This course covers the commutative aspects of abstract algebra. We start with commutative rings, in particular principal ideal domains and unique factorization domains. We then move on to the Galois theory of fields, obtaining all the major results on solvable polynomials and constructable n-gons. Finally, we consider Noetherian rings, integral extensions, Dedekind domains, and the Nullstellensatz.