## Module Handbook

• Dynamischer Default-Fachbereich geändert auf MAT

# Module MAT-43-22-M-7

## Module Identification

Module Number Module Name CP (Effort)
MAT-43-22-M-7 Algebraic Number Theory 9.0 CP (270 h)

## Basedata

CP, Effort 9.0 CP = 270 h 1 Sem. irreg. [7] Master (Advanced) [EN] English Fieker, Claus, Prof. Dr. (PROF | DEPT: MAT) Fieker, Claus, Prof. Dr. (PROF | DEPT: MAT) Malle, Gunter, Prof. Dr. (PROF | DEPT: MAT) Thiel, Ulrich, Prof. Dr. (PROF | DEPT: MAT) [MAT-AGCA] Algebra, Geometry and Computer Algebra [MAT-88.105-SG] M.Sc. Mathematics [NORM] Active

## Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
4V+2U MAT-43-22-K-7
Algebraic Number Theory
P 84 h 186 h - - PL1 9.0 irreg.
• About [MAT-43-22-K-7]: Title: "Algebraic Number Theory"; Presence-Time: 84 h; Self-Study: 186 h

## Examination achievement PL1

• Form of examination: oral examination (20-30 Min.)
• Examination Frequency: each semester
• Examination number: 86117 ("Algebraic Number Theory")

## Contents

• global fields,
• modules over Dedekind domain,
• valuation and completion,
• integral elements and orders.

## Competencies / intended learning achievements

Upon successful completion of this module, the students are familiarized with the basic concepts and methods of modern number theory. They have studied global fields and their completion and understand how these structures are related. In addition, they are able to deal independently with algorithmic problems of global fields and finite extensions.

By completing the given exercises, the students have developed a skilled, precise and independent handling of the terms, propositions and techniques taught in the lecture. They are able to name the essential propositions of the lecture as well as to classify and to explain the connections. They understand the proofs presented in the lecture and are able to comprehend and explain them. In particular, they are able to outline the conditions and assumptions that are necessary for the validity of the statements.

## Literature

• F. Lorenz: Algebra 2,
• F. Lorenz: Zahlentheorie,
• J.-P. Serre: Local Fields,
• H. Stichentoth: Algebraic Function Fields and Codes,
• H. Cohen: Advanced Topics in Computational Number Theory,
• J. Neukirch: Algebraische Zahlentheorie.

## Requirements for attendance (informal)

Additional knowledge from the module [MAT-40-29-M-4] ist useful but not necessarily required.

None

## References to Module / Module Number [MAT-43-22-M-7]

Module-Pool Name
[MAT-43-MPOOL-7] Specialisation Algebra and Number Theory (M.Sc.)
[MAT-RM-MPOOL-7] Pure Mathematics (Advanced Modules M.Sc.)