Math 551 Abstract Algebra

Fall 2010

Prof. C. Weibel
Meets TTh 3; 12:00-1:20 in H425
Main Text: N. Jacobson, Basic Algebra I, II

Homework Assignments (Fall 2010)

This is a standard course for beginning graduate students. It covers:
Group Theory10 lectures Sept.1-Oct.4 Midterm
Basic Ring & Module Theory9 lecturesOct.7-Nov.1
Modules over a PID3 lecturesNov.4-11
Bilinear Forms3 lecturesNov. 15-18,29
Artin-Wedderburn &
Maschke theorems
4 lecturesDec.2-13 Final Exam

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)

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

Last updated: November 1, 2010