Module Overview

Algebraic Structures: Rings & Fields

This module introduces the learner to the algebraic structures of Rings and Fields and to their application and uses within other scientific and mathematical areas.

Module Code

MATH 4805

ECTS Credits


*Curricular information is subject to change

Ring Theory

Basic definitions and examples, homomorphisms, isomorphisms, ideals, quotient rings, polynomial rings, divisibility and factorisation, commutative rings, integral domains, principal ideal domains, quotient field.


Field Theory

Finite fields, extension fields, simple extensions, finite extensions, minimal polynomial, construction of finite fields, primitive elements, splitting fields.

Lectures and problem-solving sessions.


Module Content & Assessment
Assessment Breakdown %
Formal Examination70
Other Assessment(s)30