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16:640:552 - Abstract Algebra II

Spring 2026

Lev Borisov

Course Description:

Math 552 is the second semester of the standard introductory graduate algebra course. A significant portion of the course is devoted to: Galois theory, commutative rings, intro to homological algebra, and representations of groups.

Text:

Algebra, by Hungerford, Thomas W.

Prerequisites:

16:640:551 or equivalent

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Spring 2025

Charles Weibel

Course Description:

Math 552 is the second semester of the standard introductory graduate algebra course. A significant portion of the course is devoted to: Galois theory, commutative rings, intro to homological algebra, and representations of groups

Text:

Hungerford (same book as used in 551)

Prerequisites:

16:640:551

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Spring 2024

Charles Weibel

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:
* Galois Theory (course notes available)
* Basic module theory: hom and tensor, projective and injective modules, Wedderburn-Artin theorom
* Commutative ring theory: Artinian and Noetherian rings
* Group Representations, semisimple modules, characters

Text:

Abstract Algebra, Dummit and Foote

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.

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Spring 2023

Charles Weibel

Course Description:

Galois Theory, Commutative rings, representations of finite groups, and Homological Algebra.

Text:

Same ass 640:551 in Fall 2022, probably Jacobson, Basic Algebra

Prerequisites:

640:551

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Spring 2022

Charles Weibel

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.

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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: