#
Math 551
Abstract Algebra

## Fall 2008

Prof. C. Weibel
Meets TTh 3; 12:00-1:20 in H425
Main Text: N. Jacobson, *Basic Algebra I, II*
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 semisimple
algebras, Artin-Wedderburn Theorem, group rings, Maschke's Theorem.
(Class supplement provided)

Homework Assignments (Fall 2008)

Prerequisites: Any standard course in abstract algebra for
undergraduate students.

Comments on this page should be sent to:
bumby@math.rutgers.edu

Last updated: September 1, 2008