This entry is from Winter semester 2016/17 and might be obsolete. You can find a current equivalent here.

# Algebra (dt. Algebra)

 Level, degree of commitment Advanced module, required module Forms of teaching and learning,workload Lecture (4 SWS), recitation class (2 SWS), 270 hours (90 h attendance, 150 h preparation and follow-up inklusive Studienleistungen, 30 h Vorbereitung and Ablegen von Prüfungsleistungen) Credit points,formal requirements 9 CP Course requirement(s): Written examination (90-120 min.) Examination type: Successful completion of at least 50% of the weekly exercises as well as at least 1-3 presentations of the tasks. Language,Grading German,The grading is done with 0 to 15 points according to the examination regulations for the degree program LAaG Mathematics. In the event of failure, a total of 4 attempts are available for the examination. Duration,frequency One semester, Jedes zweite Semester Person in charge of the module's outline Prof. Dr. Thomas Bauer, Prof. Dr. István Heckenberger, Prof. Dr. Sönke Rollenske, Prof. Dr. Volkmar Welker

## Contents

Groups: Groups and group homomorphisms, subgroups, Lagrange's theorem, normal subgroups and factor groups, isomorphism theorems, cyclic groups, main theorem on finitely generated abelian groups, permutation groups and group actions.

rings: rings and ring homomorphisms, ideals and factor rings, polynomial rings, Euclidean rings, principal ideal domains, divisibility in integral domains, quotient fields, factorial rings, polynomial rings over factorial rings

Fields: fields and field extensions, algebraic and transcendental field extensions

## Qualification Goals

Competences:

The students

• know and use algebraic forms of representation and argumentation and the formal language means of algebra with aplomb,
• understand basic principles of algebraic structures and recognize that such structures can be found in many parts of mathematics and are profitably applied there,
• know and use axiomatic procedures,
• are familiar with the problem of solving algebraic equations, know about the driving force which they represent in the history in algebra, and they know and use the results available for this purpose,
• have a deeper understanding of the implications and benefits of the algebraic structures such as group, ring and field and can explain the associated results of algebra. They understand concepts such as divisibility and factorization in an abstract context and can also use them in elementary contexts,
• have basic algebraic knowledge which is required in areas of specialization such as algebraic number theory, algebraic geometry, discrete mathematics, function theory of several variables.

Qualification goals:

Students know and use basic algebraic structures such as groups, rings and fields. They apply algebraic forms of representation and argumentation and understand axiomatic procedures.

## Prerequisites

Translation is missing. Here is the German original:

Keine. Empfohlen werden die Kompetenzen, die in den Modulen Analysis I, Analysis II und Lineare Algebra vermittelt werden

## Applicability

The module can be attended at FB12 in study program(s)

• LAaG Mathematics

When studying LAaG Mathematics, this module must be completed in the study area Advanced Modules.