Math 551 - Abstract Algebra I
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This is a standard course for beginning graduate students. It covers Group Theory, basic Ring & Module theory, and bilinear forms.
Current semester (Fall 2015)
This is a standard course for beginners. We will consider a lot of examples.
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)
Previous Semesters
- Fall 2015 (Buch)
- Fall 2014 (Carbone)
- Fall 2013 (Carbone)
- Fall 2012 (Retakh)
- Fall 2011 (Lyons)
- Fall 2010 (Weibel) Homework Assignments (Fall 2010)
- Fall 2009 (Retakh)
- Fall 2008 (Weibel) Homework Assignments (Fall 2008)
- Fall 2006 (Tunnell)
- Fall 2002 (Lyons)
- Fall 2000 (Lyons)
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