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Rings And Modules

Key information

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Module description


Basic concepts of ring theory: subrings, ideals, quotient, product, matrix and polynomial rings; factorisation in integral (euclidean, principal ideal) domains. Basic concepts of module theory: submodules, quotient modules, direct sums, homomorphisms, finitely generated, cyclic, free and torsion modules, annihilator ideals. Matrices and finitely generated modules over a principal ideal domain: Equivalence of matrices, structure theory of modules, applications to abelian groups and to vector spaces with a linear transformation.  


4CCM121A/5CCM121B Introduction to Abstract Algebra and 4CCM114A/5CCM114B Linear Algebra and Geometry II

Assessment details

Semester 1 only students will be set an alternative assessment in lieu of in-person exams in January.Full year students will complete the standard assessment.

Educational aims & objectives

This module aims to develop the general theory of rings (especially commutative ones) and then study in some detail a new concept, that of a module over a ring. Both abelian groups and vector spaces may be viewed as modules and important structure theorems for both follow from the general theory. The theory of rings and modules is key to many more advanced algebra courses e.g. Algebraic Number Theory. It can also help with others, e.g. Galois Theory, Representation Theory and Algebraic Geometry.

Teaching pattern

Three hours of lectures and one hour of tutorial per week throughout the term

Suggested reading list

Indicative reading list - link to Leganto system where you can search with module code for lists

Module description disclaimer

King’s College London reviews the modules offered on a regular basis to provide up-to-date, innovative and relevant programmes of study. Therefore, modules offered may change. We suggest you keep an eye on the course finder on our website for updates.

Please note that modules with a practical component will be capped due to educational requirements, which may mean that we cannot guarantee a place to all students who elect to study this module.

Please note that the module descriptions above are related to the current academic year and are subject to change.