This is a standard course for second semester graduate students. It covers fields and Galois Theory, basic Ring & Module theory, and elementary homological algebra.
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.
- 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)
Last updated: May 21, 2015
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Information posted prior to the beginning of the semester is frequently tentative, or based on previous semesters. Textbooks should not be purchased until confirmed with the instructor. For generally reliable textbook information—with the exception of sections with an alphabetic code like H1 or T1, and topics courses (197,395,495)—see the textbook list.