# Groups and Rings

Course Code : | 1001WETGRC |

Study domain: | Mathematics |

Academic year: | 2017-2018 |

Semester: | 2nd semester |

Contact hours: | 60 |

Credits: | 6 |

Study load (hours): | 168 |

Contract restrictions: | No contract restriction |

Language of instruction: | Dutch |

Exam period: | exam in the 2nd semester |

Lecturer(s) | Karim Johannes Becher |

### 1. Prerequisites *

- competences corresponding the final attainment level of secondary school

an active knowledge of

- Dutch

- English

Knowledge of the course 'Lineaire Algebra'

### 2. Learning outcomes *

- The student is familiar with basic concepts of algebra such as groups, (commutative) rings and fields and knows general structure theorems as well as motivating examples.

### 3. Course contents *

Basic Group Theory:

- Isomorphism theorems, order of a group, normal subgroups, index of a subgroup (Lagrange's Theorem)

- Classification of finite abelian groups

- Permutations

- Group actions, Sylow Theorems

Basic Ring Theory:

- ideals, modules, quotients

- principal ideal domains, factorial domains, polynomial rings

- prime ideals, maximal ideals, Zorn's Lemma and Krull's Theorem

### 4 International dimension*

### 5. Teaching method and planned learning activities

Personal work

### 6. Assessment method and criteria

The intermediate test and the participation cannot be repeated. In the case where the resit exam is taken, the final grade for the second session is computed in the same way (see 5.3), on the basis of the original grades for participation and the test.

Examination

Continuous assessment

### 7. Study material *

#### 7.1 Required reading

Course notes will be provided.

**7.2 Optional reading**

The following study material can be studied voluntarily :### 8. Contact information *

Karim Johannes Becher (office G.224); email: karimjohannes.becher@uantwerpen.be

Nikolaas Verhulst (office G.308); email: nikolaas.verhulst@uantwerpen.be