Module manager: Michael Wibmer
Email: m.wibmer@leeds.ac.uk
Taught: Semester 2 (Jan to Jun) View Timetable
Year running 2025/26
| MATH1000 | Core Mathematics |
MATH2027
This module is not approved as a discovery module
Rings, like groups, are one of the fundamental concepts of abstract algebra and they play a key role in many areas, including number theory, algebraic geometry, Galois theory and representation theory. The aim of this module is to give an introduction to rings. The emphasis will be on interesting examples of rings and their properties.
The module introduces students to the theory of rings, thereby preparing them for further study in abstract algebra. Throughout the course polynomial rings will be used to illustrate important concepts.
On successful completion of the module students will have demonstrated the following learning outcomes:
1. Explain the main concepts of ring theory introduced in the module.
2. Determine elementary properties of a given ring, and its elements
3. Carry out simple computations in elementary rings
4. Determine whether a given subset of a ring is a subring or ideal
5. Give examples of rings, subrings or ideals with given properties
6. Apply the First Isomorphism Theorem for rings
7. Write proofs within an axiomatic framework
Skills Learning Outcomes
On successful completion of the module students will have demonstrated the following skills learning outcomes:
a. Apply analytical thinking and technical knowledge to solve problems.
b. Communicate technical information using written and spoken media.
c. Maintain and uphold academic integrity and professional ethics.
d. Manage workload and deadlines through prioritisation and productivity skills.
1. Introduction to the main concepts of ring theory
2. Key examples of rings and fields
3. Subrings and ideals
4. First Isomorphism Theorem
5. Euclidean domains, principal ideal domains and unique factorisation domains
6. Greatest common divisors and factorisation
Additional topics that build on these may be covered as time allows. Such topics may be drawn from the following, or similar:
7. Algebras
8. Prime and maximal ideals
9. Simple field extensions
10. Tests for irreducibility of polynomials
11. The field of quotients of an integral domain
Methods of assessment
The assessment details for this module will be provided at the start of the academic year
| Delivery type | Number | Length hours | Student hours |
|---|---|---|---|
| Lecture | 11 | 2 | 22 |
| Seminar | 5 | 1 | 5 |
| Private study hours | 73 | ||
| Total Contact hours | 27 | ||
| Total hours (100hr per 10 credits) | 100 | ||
Regular written formative coursework with feedback to students.
The reading list is available from the Library website
Last updated: 30/04/2025
Errors, omissions, failed links etc should be notified to the Catalogue Team