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Ingo Runkel
Algebra Seminar (Rings and Modules) - Summer term 2012
Ankündigungen:
Verteilung der Vorträge:
- 3.4 : Vorbesprechung und Grundlagen (IR)
- 10.4 : Grundlagen (IR)
- 17.4 : Dies Academicus - Seminar fällt aus
- V6 (24.4) : Kettenbedingungen (AO)
[pdf]
- V7 (8.5) : Jordan-Hölder (YK)
[pdf]
- V8 (15.5/22.5) : Zerlegung von Ringen (SW)
[pdf]
- V9 (22.5/5.6) : Wedderburn-Artin (CL)
[pdf]
- V10 (5.6/12.6) : Hom Funktor und Exaktheit (ID)
[pdf]
- V11 (12.6/19.6) : Projektiv und injektiv (SN)
[pdf]
- V12 (26.6) : Tensorprodukt Funktor (IR)
- V13 (3.7) : Rechtsexakt und Tensorprodukt (CN)
[pdf]
Description:
In this seminar we discuss a selection of topics in ring theory
and in the theory of modules. These appear as foundations in many
other areas such as representation theory, homological
algebra or algebraic geometry. A rough overview of topics treated is
- division rings (Wedderburn's Little Theorem, Frobenius' Theorem)
- basics on modules (sums and products, generators and cogenerators, socle and radical)
- chain conditions (noetherian and artinian modules, Jordan Hölder Theorem)
- semi-simple rings (Wedderburn-Artin Theorem)
- Hom and tensor functors (projective/injective/flat modules, exactness)
- Morita equivalence
A more detailed description of the individual seminar talks is
available here [pdf].
In the Winter Term 2011/12 we treated Lie Algebras in the
Advanced Algebra class. The above topics constitute and
alternative standard content of an Advanced Algebra
class and will be useful to students with an interest in algebraic
topics.
This course is aimed at Masters students and third year Bachelor students.
Prerequisites:
Basic notions from algebra (in particular groups, fields,
linear algebra); the module "Algebra 1" is recommended.
Literature:
- Anderson, Fuller, Rings and categories of modules, Springer 1992.
- Farb, Dennis, Noncommutative Algebra, Springer 1993.
- Jantzen, Schwermer, Algebra, Springer 2005.
- Lam, A first course in noncommutative rings, Springer 2001.
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