Algebraic Number Theory

Education facts

Code: MMA350

Algebraic number theory is the part of number theory that uses methods from algebra to answer questions about integers in general and number fields in particular. The subject has inspired the Langlands Program, which won the Abel Prize, and is fundamental to parts of algebraic geometry. An important concept is algebraic integers, which concern the relationship between ordinary integers and rational numbers. But in most number fields, unique factorization of integers as a product of primes does not work. In this course you will study algebraic integers and fractional ideals which work as "ideal numbers" in number fields. You will also learn how different factorization of ideals and integers can be.

Entry requirements

General entry requirements and the equivalent of 90credits in mathematics and basic Galois theory equivalent to parts of the course MMA310 Galois Theory. In Galois theory, the requirements are: knowledge of separable field extensions, the fundamental theorem of Galois theory, the existence of the algebraic extension of the rational numbers, and the embedding of number fields therein.

Education offerings

Each offering has its own dates and conditions. Closed offerings are retained as history and do not mean that a new application is open.

• Algebraic Number Theory

  University of Gothenburg

  GÖTEBORG

  Start date: 17 January 2028

  End date: 22 March 2028

  Pace of study: 50 %