Course Descriptions

16:640:552 - Abstract Algebra II

Spring 2021 - Jerrold Tunnell

Course Description:

This is the continuation of Math 551, aimed at a discussion of many fundamental algebraic structures. The course will cover the following topics (and perhaps some others). Basic module theory and introductory homological algebra - most of Chapter 3 and part of Chapter 6 of Basic Algebra II: hom and tensor, projective and injective modules, abelian categories, resolutions, completely reducible modules, the Wedderburn-Artin theorem Commutative ideal theory and Noetherian rings - part of Chapter 7 of Basic Algebra II: rings of polynomials, localization, primary decomposition theorem, Dedekind domains, Noether normalization Galois Theory - Chapter 4 of Basic Algebra I and part of Chapter 8 of Basic Algebra II: algebraic and transcendental extensions, separable and normal extensions, the Galois group, solvability of equations by radicals

Text:

Jacobson, "Basic Algebra", Volumes 1 and 2, second edition.

Prerequisites:

Any standard course in abstract algebra for undergraduates and/or Math 551. It will be assumed that students understand the concepts of groups, rings, modules, vector space and linear algebra, and finitely generated modules over principal ideal domains.

Schedule of Sections:

Previous Semesters: