Algebra - MATH702
This unit provides an advanced introduction to key areas of research interest in modern algebra. It will centre around the theory and applications of modules over a ring. Modules are a common generalisation of the notions of vector space over a field, of abelian group, of group representation, and of square matrix. We will see how to extend some of the theory of these notions developed in undergraduate years to the setting of modules. An important recurring idea will be that of a structure theorem, such as the undergraduate-level result that every finitely-generated abelian group is a direct sum of cyclic groups. We shall see various structure theorems for the various algebraic notions studied, with an important example being the Wedderburn theorem for semi-simple rings. Applications to representation theory will be particularly emphasised.
| Credit Points: | 4 |
| When Offered: | S1 Day - Session 1, North Ryde, Day |
| Staff Contact(s): | Mathematics staff |
| Prerequisites: |
Admission to MRes |
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| Assessed As: | Graded |
| Offered By: | Department of Mathematics Faculty of Science and Engineering |
Course structures, including unit offerings, are subject to change.
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