Course Code : | 1600WETRMO |

Study domain: | Mathematics |

Academic year: | 2019-2020 |

Semester: | 1st semester |

Contact hours: | 60 |

Credits: | 6 |

Study load (hours): | 168 |

Contract restrictions: | No contract restriction |

Language of instruction: | Dutch |

Exam period: | exam in the 1st semester |

Lecturer(s) | Wendy Lowen |

At the start of this course the student should have acquired the following competences:

an active knowledge of

- competences corresponding the final attainment level of secondary school

an active knowledge of

- Dutch

- The student masters the content of the course (knows the concepts and results and can prove them) and can apply his or her insight in the material in new situations (making new exercises, finding and proving new related results, ...).

Chapter 1 - Rings and ideals: we develop the basic theory of (not necessarily commutative) rings. Topics: posets and Zorn's Lemma, rings and ideals, quotients, prime and maximal ideals, Noetherian rings, the Chinese remainder theorem, localisation (commutative).

Chapter 2 - Modules: basic notions, projective and injective modules, tensor product and flat modules, finitely generated modules, exact rows and diagram chasing.

Chapter 3 - Commutative rings: we develop the theory in close connection with the elements of algebraic geometry. Topics include: the spectrum, Hilbert's Nulstellensatz, local rings, dimension.

Class contact teachingLectures Practice sessions

ExaminationWritten examination without oral presentation Written with oral presentation Oral with written preparation Closed book Open-question

Course notes

M.F. Atiyah, I.G. Macdonald, Introduction to Commutative Algebra, Addison-Wesley Publ. Co. Inc., Reading Massachusetts

H. Matsumura, Commutative ring theory, Cambridge studies in advanced mathematics 8, Cambridge University press

D. Eisenbud, Commutative algebra with a view towards algebraic geometry, Graduate Texts in Mathematics, Springer

J.C. McConnell and J.C. Robson, Noncommutative Noetherian rings, Pure and Applied MAthematics, Wiley

Wendy Lowen: wendy.lowen@uantwerpen.be

Arne Mertens: arne.mertens@uantwerpen.be