Plan/log

Date Themes Reference
Log of what we have covered and what we plan to do:
19.08 (Wednesday) Plan: Introduction, definitions, various examples of rings (polynomial rings, ring of group endomorphisms, Boolean rings), and basic properties of rings. Chap 9.1, 9.2, 9.3
26.08 (Wednesday) Plan: Subrings, characteristic of a ring, idempotent and nilpotent elements, (left, right, and 2-sided) ideals, homomorphisms, intersections of ideals Chap 9.4, 9.5, 10.1
28.08 (Friday) Present problem set 1 during first half of class. Fundamental theorem of ring homomorphisms, ideal correspondence theorem, sum and direct sum of ideals Chap 10.2, 10.3
02.09 (Wednesday) maximal and prime ideals, nilpoten and nil ideals, Zorns lemma Chap 10.4, 10.5, 10.6
04.09 (Friday) Unique factorization domains, Principal ideal domains Chap 11.1, 11.02
09.09 (Wednesday) Euclidian domains, polynomial rings over UFD Chap 11.3, 11.4
11.09 (Friday) Polyniomial rings over UFD, rings of fractions of a commutative domain, modules chap 11.4, 12.1, 14.1
16.09 (Wednesday) presented problem set 2 and 3, Modules, submoduler and direct sum Chapter 14.1, 14.2
18.09 (Friday) R-homomorphisms between left moduler, quotient module, simple modules and completly reducilble (semisimple )modules. Chapter 14.3, 14.4
23.09 (Wednesday) Give solutions to problemset 4. Finish simple-, semisimple- (completely reducible) and free modules, and may start on Noetherian and Arinian modules. Chapter 14.3, 14.4, 14.5, 19
25.09 (Friday) Finisch Chapter 14 (semisimple modules), and start on Chapter 19 about noetherian and artinian modules and rings Chapter 14.4, 19.1, 19.2
30.09 (Wednesday) went through problems, chapter 19.2.1,2,3,4,5,6,7,8 and started on 19.2.14 chapter 19.2
02.10 (Friday) Finish Chapter 19.2 and start on chapter 19.3 and give some more examples Chap. 19.2,19.3
07.10 (Wednesday) Discuss problem set 6 and finish Chapter 19.3 Chapter 19.3
09.10 (Friday) Finished Chapter 19.3, inclusive a different proof for theorem 19.3.5 Chapter 19.3
13.10 (Wednesday) Discuss problem set 7 and start on chapter 20 Chapter 20
2020-10-12, Sverre Olaf Smalø