Mathematics 612 - Algebra II

A continuation of Math 611. Topics in group theory (e.g., Sylow theorems, solvable and simple groups, Jordan-Holder and Schreier theorems, finitely generated Abelian groups). Topics in ring theory (matrix rings, prime and maximal ideals, Noetherian rings, Hilbert basis theorems). Modules, including cyclic, torsion, and free modules, direct sums, tensor products. Algebraic closure of fields, normal, algebraic, and transcendental field extensions, basic Galois theory. Prerequisite: Math 611 or equivalent.

Open to Graduate students only.