742 - Abstract Algebra II

Math 742 is the second half of the basic first-year graduate course in abstract algebra. It stresses the commutative aspects of the subject and consists of two main parts. The first part concerns commutative Noetherian rings and includes the Hilbert basis theorem and Nullstellensatz, the Lasker-Noether theorem, the Krull intersection theorem and the principal ideal theorem. The second part concerns field theory and includes Galois theory, constructability of geometric objects, solvability of polynomials, algebraic number fields and Dedekind domains.