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Course Descriptions

16:640:551 - Abstract Algebra I

Anders Buch

Text: 

Notes in preparation by Jonathan Brundan and Alexander Kleshchev

Prerequisites:

Standard course in Abstract Algebra for undergraduate students at the level of our Math 451.

Description:

This is a standard course for beginning graduate students. It covers Group Theory, basic Ring & Module theory, and bilinear forms. Group Theory: Basic concepts, isomorphism theorems, normal subgroups, Sylow theorems, direct products and free products of groups. Groups acting on sets: orbits, cosets, stabilizers. Alternating/Symmetric groups. Basic Ring Theory: Fields, Principal Ideal Domains (PIDs), matrix rings, division algebras, field of fractions. Modules over a PID: Fundamental Theorem for abelian groups, application to linear algebra: rational and Jordan canonical form. Bilinear Forms: Alternating and symmetric forms, determinants. Spectral theorem for normal matrices, classification over R and C. (Class supplement provided) Modules: Artinian and Noetherian modules. Krull-Schmidt Theorem for modules of finite length. Simple modules and Schur's Lemma, semisimple modules. (from Basic Algebra II) Finite-dimensional algebras: Simple and sem isimple algebras, Artin-Wedderburn Theorem, group rings, Maschke's Theorem.

Note: A Problem Session for 551 will be held on Wednesdays, 5:00pm-6:20pm in room 423 for the Fall semester. There is no need to register for the Problem Sessions.


Sections Taught This Semester:

For more information on instructors and sections for Fall 2017, please see our Fall 2017 Teaching Schedule Page

For more information on instructors and sections for this course for other semesters, please see our Teaching Schedule Page


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Department of Mathematics

Department of Mathematics
Rutgers University
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