Schedule
| date | subject | references
|
|---|
| Sep 2 | Overview (hwl);
infinite Galois theory (bds) |
| | Sep 9 | Profinite groups and infinite Galois Theory
(bds)
| | Sep 16 | Grothendieck's formulation of Galois theory;
transcendence degree;
purely inseparable extensions
(bds) |
| | Sep 23 | Tensor products
(hwl) |
Tensor products: Atiyah-Macdonald, Introduction to commutative
algebra, Chapter 2 and Lang's Algebra Chapter XVI (both over
commutative rings only), Bourbaki, Algebra 1, Chapter II,
section 3.
| | Sep 30 | no class |
| | Oct 7 |
Semilinear group actions
(hwl) |
Semilinear group actions: Bourbaki, Algebra 2, Chapter V
(Commutative fields), section 10, nr. 4 (Galois descent).
Hilbert 90: Lang's Algebra, Chapter VI, section 10;
| | Oct 14 | Kummer theory (bds) |
| | Oct 21 | Normal basis theorem (hwl) |
Normal basis theorem: Jacobson, Basic algebra I, section 4.14.
Normal basis theorem for infinite Galois extensions:
www.math.leidenuniv.nl/~hwl/PUBLICATIONS/1985c/art.pd
Indecomposable modules and the theorem of Krull-Remak-Schmidt:
Lang's Algebra, Chapter X, section 7.
| | Oct 28 | Differentials (bds) |
Matsumura, Commutative ring theory, sections 25, 26;
Jacobson, Basic Algebra II, sections 8.15, 8.16.
| | Nov 4 | no class |
| | Nov 11 | End of proof of theorem of Krull-Remak-Schmidt,
proof of the normal basis theorem, real closed fields (hwl) |
Real closed fields: Lang, Algebra, Chapter XI;
Emil Artin, Collected papers, nr. 21; Alexander Tonkelaar,
Reëel afgesloten lichamen (
bachelorscriptie, in Dutch)
| | Nov 18 | Separable extensions (bds) |
Matsumura, Commutative ring theory, sec 26.
| | Nov 25 | Semisimple modules, density theorem, Jacobson-Bourbaki correspondence (bds) | Jacobson, Basic Algebra, sections 3.5, 4.3, 8.2
| | Dec 2 | Real closed fields (hwl) |
| | Dec 9 | Real closed fields (hwl) |
|
Last update November 25, 2013, 15:23 |