For a given field F we seek all division algebras over F up to isomorphism. This question was first investigated for division algebras of finite dimension over F by Richard Brauer. We discuss the construction of the Brauer group and some examples. Crossed products and PI algebras are then introduced with a focus on Amitsur's non-crossed product algebra. Finally, we look at some modern results of Bell on the Gelfand-Kirillov dimension of finitely generated algebras over F and the classification of their division subalgebras.
| Identifer | oai:union.ndltd.org:WATERLOO/oai:uwspace.uwaterloo.ca:10012/4072 |
| Date | January 2008 |
| Creators | Ashburner, Michelle Roshan Marie |
| Source Sets | University of Waterloo Electronic Theses Repository |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
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