Commutative Algebra (KomAlg), E2011

Opslag 18. januar 2012
Så er OBL2 klar, igen lidt sent i forhold til fristen: Afleveres den 25/1 til instruktoren.
Opslag 22. december 2011
Aflysning: Forelæsningerne den 2. januar 2012 er aflyst, men ikke hjemmearbejdet. Jeg regner med at deltagerne inden onsdag den 4. januar selv har læst NOETH3. Bemærk, at undervisningsplanen er udvidet: NOETH5 er tilføjet til uge 6. Gennemgangen af NOETH5 bliver meget kursorisk.
Opslag 7. december 2011
Så er OBL1 klar, noget forsinket. Afleveres den 14/12 til instruktoren.
Du kan finde gotiske bogstaver HER!

Welcome to the 2011 web page for Commutative Algebra. Web master for this external page, and responsible for the course, is Anders Thorup. The page will be updated during the course.

Information.
SIS-info.

Schema.
Teaching period: Blok 2, skema C; 9 weeks: 21 November -- 21 December 2011, 2 January -- 25 January 2012.
Lectures by Anders Thorup:
   Monday 12:15-15:00 in Aud 6 and Wednesday 10:15-12:00 i Aud. 10.
Excercise sessions with Angela Klamt   <angela@math.ku.dk>, tlf 35320679:
   Wednesday 13:15-16:00 in RF062 (NBI).

Assessment.
Continuous assessment, internal censorship, 7-grade scale. The grade is given for two cumpulsory homework assignments (in week numbers 4 and 9) and one 2 hours written test (in week number 7). Re-examination: Oral examination 18 April 2012.

Material.
There is a set of lecture notes written for the 2005 version of the course in Danish: komalg.pdf. A slightly corrected version will appear before the start of the course. With sufficiently many participants it will be published in the "IMF Notes" series.

Even if you don't read Danish, you may (combined with the lectures given in English) be able to read the Danish Mathematics of the lecture notes. An English reference is the following:
Rodney Y. Sharp,
"Steps in Commutative Algebra," (2. ed),
London Mathematical Society Student Texts (No. 51)
Cambridge University Press, Cambridge 2001,
ISBN: 9780521646239

Plan.
Below is the intended plan of the course. Remember, it's only a plan, and plans may be changed.

Week Headline Refs Exercises
1 Rings and Modules RM 1, 2, 3 RM1: 1, 2, 4, 5, 9
2 Rings and Modules RM 3, 4 RM1: 10, 12, 13, 14, 16, 17, 23; RM2: 4
3 Finiteness ENDL 1, 2, 3, 4 RM1: 25, 26; RM2: 5; RM3: 3, 4, 5, 6; RM4: 1, 2, 3
4 Finiteness. Noetherian Modules ENDL 4; NOETH 1, 2 OBL1; ENDL1: 1, 2, 4; ENDL2: 1, 2, 4; ENDL3: 1, 2, 3, 4
5 Noetherian Modules ENDL 5; NOETH 1, 2 ENDL1: 5; ENDL2: 9; ENDL3: 5, 6, 7, 12, 13
6 Noetherian Modules NOETH 3, 4, 5 RM1: 32; RM4: 11, 13; ENDL1: 6; ENDL3: 4, 8; NOETH1: 2, 4, 5
7 Dimension Theory NOT 1, 2, DIM 1, 2. TEST; RM4: 7; NOETH1: 6; NOETH2: 1, 4; NOETH3: 1, 2, 3, 5
8 Dimension Theory NOT 3, DIM 2, 3. ENDL2: 5; NOETH1: 9; NOETH3: 7, 10, 11, 12, 13,
9 Dimension Theory DIM 3, 4, 5 OBL2; RM1: 36; RM3: 14, 16; RM4: 12; ENDL1: 9; ENDL4: 3, 4, 6; NOT1: 1
OBL=Compulsary Home work is handed in on Wednesday.

Week	Headline	Refs	Exercises
1	Rings and Modules	RM 1, 2, 3	RM1: 1, 2, 4, 5, 9
2	Rings and Modules	RM 3, 4	RM1: 10, 12, 13, 14, 16, 17, 23; RM2: 4
3	Finiteness	ENDL 1, 2, 3, 4	RM1: 25, 26; RM2: 5; RM3: 3, 4, 5, 6; RM4: 1, 2, 3
4	Finiteness. Noetherian Modules	ENDL 4; NOETH 1, 2	OBL1; ENDL1: 1, 2, 4; ENDL2: 1, 2, 4; ENDL3: 1, 2, 3, 4
5	Noetherian Modules	ENDL 5; NOETH 1, 2	ENDL1: 5; ENDL2: 9; ENDL3: 5, 6, 7, 12, 13
6	Noetherian Modules	NOETH 3, 4, 5	RM1: 32; RM4: 11, 13; ENDL1: 6; ENDL3: 4, 8; NOETH1: 2, 4, 5
7	Dimension Theory	NOT 1, 2, DIM 1, 2.	TEST; RM4: 7; NOETH1: 6; NOETH2: 1, 4; NOETH3: 1, 2, 3, 5
8	Dimension Theory	NOT 3, DIM 2, 3.	ENDL2: 5; NOETH1: 9; NOETH3: 7, 10, 11, 12, 13,
9	Dimension Theory	DIM 3, 4, 5	OBL2; RM1: 36; RM3: 14, 16; RM4: 12; ENDL1: 9; ENDL4: 3, 4, 6; NOT1: 1