Course Schedule and Catalog

Long Title: ADVANCED ALGEBRA II

Department: Mathematics

Grade Mode: Standard Letter

Language of Instruction: Taught in English

Course Type: Lecture

Credit Hours: 3

Prerequisite(s): MATH 463 OR MATH 563

Description: A continuation of Math 563. Integrality: going up and down theorems. Noether Normalization and Hilbert's Nullstellensatz. Artinian Rings, Discrete Valuation Rings and Dedekind Domains, with applications: rings of integers in number rings, prime decomposition in number ring extensions. Completions: topologies, filtrations. Graded modules and associated graded rings. Homological algebra: complexes, homology, homotopies; injective, projective and flat modules. Derived functors: Ext and Tor. Introduction to group cohomology and spectral sequences. Graduate/Undergraduate Equivalency: MATH 464. Mutually Exclusive: Cannot register for MATH 564 if student has credit for MATH 464.