## BMS Basic Course Commutative Algebra - Algebra II (32428)

#### Lectures: Prof. Dr. Jürg Kramer

Contents: Noetherian, factorial and polynomial rings; modules; elements of homological and multilinear algebra; algebras over fields, like semi-simple and simple matrix algebras

#### Exercises: Olaf Teschke

• Timetable: Wednesday, 09.15 -10.45
• Location: Rudower Chaussee 25, House 1, Room 1.011
• Office hour: Thursday, 13-15, RUD 25, 2.304 or same floor
• !Note! In the exam's week, there is an additional office hour Tuesday, 5th, 13-15

#### Problem Sets

Points (please check that the entries are correct)

1. No. 1 (hand in Oct 25th)
2. No. 2(hand in Nov 1st)
3. No. 3 (hand in Nov 8th)
4. Halloween Problem (voluntary, hand in at 2.304 whenever you like)
5. No. 4 (hand in Nov 15th)
6. No. 5 (hand in Nov 22nd)
7. No. 6 (hand in Nov 29th)
8. No. 7 (hand in Dec 6th)
9. Advent problem (for Christmas season & New Year's break; hand in till 2008, Jan 10th)
10. No. 8 (hand in Dec 13th)
11. No. 9 (hand in Dec 20th)
12. Correction: In the definition of 3), on should use the projective limit instead of the direct one.Therefore, 3 becomes a 3* problem.
13. No. 10 (hand in Jan 10th)
14. Due to the correction in No. 9, 4a) is deleted (additional points may be awarded if the problem has been approached)
15. No. 11 (hand in Jan 17th)
16. No. 12 (hand in Jan 24th)
17. Set 12, problem 3a) is deleted.
18. No. 13 (hand in Jan 31st)
19. Voluntary peraration set (hand in Feb 6th - but in case of urgent need of points, a delay by a few days should be acceptable)

#### Selected Literature

• Michael F. Atiyah, I.G. MacDonald, Introduction to Commutative Algebra. Addison-Wesley (1969; Zbl 0175.03601)
• Hideyuki Matsumura. Commutative Algebra. 2nd ed. Math. Lect. Notes Ser. 56 (1980; Zbl 0441.13001)
• Nicolas Bourbaki. Elements of Mathematics. Commutative Algebra. Chapters 1-7. Transl. from the French. Springer xxiv (2006; Zbl 0902.13001)
• George R. Kempf, Algebraic Structures. Vieweg Verlag (1995; Zbl 0831.00002)
• David Eisenbud, Commutative Algebra. With a View Toward Algebraic Geometry. Graduate Texts in Mathematics 150 (1995; Zbl 0819.13001)
• R. Elkik, Cours d'algebre. Paris: Ellipses (2002; Zbl 1119.00001)

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