*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 |