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Algebraic Number Theory (MSc) - MAT00071H

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  • Department: Mathematics
  • Module co-ordinator: Dr. Evgeniy Zorin
  • Credit value: 10 credits
  • Credit level: H
  • Academic year of delivery: 2022-23
    • See module specification for other years: 2021-22

Module summary

This module is for postgraduate students only.

Related modules

Pre-requisite modules

  • None

Co-requisite modules

  • None

Prohibited combinations

Additional information

Students should have seen a first course in Groups, Rings and Fields.

Module will run

Occurrence Teaching period
A Autumn Term 2022-23

Module aims

To introduce the concept of algebraic numbers, and study their existence and properties.

Module learning outcomes

At the end of this module you should be able to understand:

  • The concept (definition and significance) of algebraic numbers and algebraic integers.
  • How to factorise an algebraic integer into irreducibles.
  • How to find the ideals of an algebraic number ring.
  • The definition of the Class Group.

Module content


  • Algebraic Numbers, including bases, norm, trace, and the ring of integers.
  • Modules, Integral Dependence and Noetherian Domains.
  • Factorisation in rings of integers, discriminant, examples of uniqueness and non-uniqueness of factorisation.
  • Factorisation of ideals, the Class Group and the Class Number.


Task Length % of module mark
Closed/in-person Exam (Centrally scheduled)
Algebraic Number Theory
2 hours 100

Special assessment rules



Task Length % of module mark
Closed/in-person Exam (Centrally scheduled)
Algebraic Number Theory
2 hours 100

Module feedback

Current Department policy on feedback is available in the undergraduate student handbook. Coursework and examinations will be marked and returned in accordance with this policy.

Indicative reading

I Stewart & D Tall, Algebraic Number Theory and Fermat’s Last Theorem, Fourth Edition Taylor & Francis (2015).

The information on this page is indicative of the module that is currently on offer. The University is constantly exploring ways to enhance and improve its degree programmes and therefore reserves the right to make variations to the content and method of delivery of modules, and to discontinue modules, if such action is reasonably considered to be necessary by the University. Where appropriate, the University will notify and consult with affected students in advance about any changes that are required in line with the University's policy on the Approval of Modifications to Existing Taught Programmes of Study.