# 401-3132-00L Commutative Algebra

Semester | Autumn Semester 2018 |

Lecturers | P. D. Nelson |

Periodicity | yearly recurring course |

Language of instruction | English |

### Courses

Number | Title | Hours | Lecturers | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

401-3132-00 V | Commutative Algebra | 4 hrs |
| P. D. Nelson | |||||||||

401-3132-00 U | Commutative Algebra | 1 hrs |
| P. D. Nelson |

### Catalogue data

Abstract | This course provides an introduction to commutative algebra as a foundation for and first steps towards algebraic geometry. |

Objective | We shall cover approximately the material from --- most of the textbook by Atiyah-MacDonald, or --- the first half of the textbook by Bosch. Topics include: * Basics about rings, ideals and modules * Localization * Primary decomposition * Integral dependence and valuations * Noetherian rings * Completions * Basic dimension theory |

Literature | Primary Reference: 1. "Introduction to Commutative Algebra" by M. F. Atiyah and I. G. Macdonald (Addison-Wesley Publ., 1969) Secondary Reference: 2. "Algebraic Geometry and Commutative Algebra" by S. Bosch (Springer 2013) Tertiary References: 3. "Commutative algebra. With a view towards algebraic geometry" by D. Eisenbud (GTM 150, Springer Verlag, 1995) 4. "Commutative ring theory" by H. Matsumura (Cambridge University Press 1989) 5. "Commutative Algebra" by N. Bourbaki (Hermann, Masson, Springer) |

Prerequisites / Notice | Prerequisites: Algebra I (or a similar introduction to the basic concepts of ring theory). |

### Performance assessment

Performance assessment information (valid until the course unit is held again) | |

Performance assessment as a semester course | |

ECTS credits | 10 credits |

Examiners | P. D. Nelson |

Type | session examination |

Language of examination | English |

Repetition | The performance assessment is offered every session. Repetition possible without re-enrolling for the course unit. |

Mode of examination | oral 30 minutes |

This information can be updated until the beginning of the semester; information on the examination timetable is binding. |

### Learning materials

Main link | Lecture Homepage |

Only public learning materials are listed. |

### Groups

No information on groups available. |

### Restrictions

There are no additional restrictions for the registration. |

### Offered in

Programme | Section | Type | |
---|---|---|---|

Mathematics Bachelor | Core Courses: Pure Mathematics | W | |

Mathematics Master | Core Courses: Pure Mathematics | W |