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Semigroup Theory - MAT00050M

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  • Department: Mathematics
  • Module co-ordinator: Prof. Victoria Gould
  • Credit value: 10 credits
  • Credit level: M
  • Academic year of delivery: 2017-18

Module will run

Occurrence Teaching cycle
A Autumn Term 2017-18

Module aims

A semigroup is a set together with an associative binary operation. Fundamental examples abound: consider the set T_X of all functions from a set X to itself and M_ n(R) with operations composition of functions and matrix multiplication, respectively.

The aim of the course is to familiarise students with the elementary notions of semigroup theory. Abstract ideas will be illustrated by applying them to semigroups such as T_X, M_n(R) and the bicyclic semigroup B . The course will move on to study Green's relations and how these may be used to develop structure theorems for semigroups

Module learning outcomes

At the end of the module you should be familiar with:

the basic ideas of the subject, including Green's relations, and to be able to handle the algebra of semigroups in a comfortable way;

the role of structure theorems and to be able to use Rees' theorem for completely 0-simple semigroups;

to have an appreciation of the place of semigroup theory in mathematics.


Task Length % of module mark
University - closed examination
Semigroup Theory
2 hours 100

Special assessment rules



Task Length % of module mark
University - closed examination
Semigroup Theory
2 hours 100

Module feedback

Information currently unavailable

Indicative reading

J M Howie, Fundamentals of Semigroup Theory, Oxford: Clarendon Press (S 2.86 HOW).
Other texts will be discussed at the start of the course

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.