This is a standard course for second semester graduate students. It covers fields and Galois Theory, basic Ring & Module theory, and elementary homological algebra.
Algebra I (640:551) or its equivalent
Basic Field Theory: Galois groups, separable and inseparable extensions, solutions of equations, finite fields.
Noetherian rings: chain conditions, Hilbert Basis Theorem, Noether normalization, Hilbert Nullstellensatz.
Basic module theory: Tensor Product, Projective and injective modules, resolutions, baby homological algebra.
Finite-dimensional algebras: Simple and semisimple algebras, Artin-Wedderburn Theorem, group rings.
Main Text: N. Jacobson, Basic Algebra I, II
Last Updated: May 2015
- Spring 2017 (Tunnell)
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
- Spring 2016 (Weibel)
- Spring 2015 (Retakh)
- Spring 2014 (Lyons)
- Spring 2013 (Tunnell)
- Spring 2012 (Buch)
- Spring 2011 (Wilson)
- Spring 2010 (Weibel)
- Spring 2009 (Vasconcelos)
- Spring 2008 (Wilson)
- Spring 2007 (Retakh)
- Spring 2006 (Thomas)
- Spring 2005 (Wilson)
- Spring 2004 (Vasconcelos)
- Spring 2003 (Knop)
- Spring 2002 (Vasconcelos)