MT5863 Semigroups

Academic year

2023 to 2024 Semester 2

Further information on which modules are specific to your programme.

Key module information

SCOTCAT credits

15

The Scottish Credit Accumulation and Transfer (SCOTCAT) system allows credits gained in Scotland to be transferred between institutions. The number of credits associated with a module gives an indication of the amount of learning effort required by the learner. European Credit Transfer System (ECTS) credits are half the value of SCOTCAT credits.

SCQF level

SCQF level 11

The Scottish Credit and Qualifications Framework (SCQF) provides an indication of the complexity of award qualifications and associated learning and operates on an ascending numeric scale from Levels 1-12 with SCQF Level 10 equating to a Scottish undergraduate Honours degree.

Planned timetable

1pm Monday, Thursday, Friday

This information is given as indicative. Timetable may change at short notice depending on room availability.

Module coordinator

Prof J D Mitchell

Prof J D Mitchell
This information is given as indicative. Staff involved in a module may change at short notice depending on availability and circumstances.

Module description

The general aim of this module is to introduce students to semigroup theory, which is the study of sets with one associative binary operation defined on them. In the process, the common aims and concerns of abstract algebra will be emphasised and illustrated by drawing comparisons between semigroups, groups and rings

Relationship to other modules

Pre-requisites

BEFORE TAKING THIS MODULE YOU MUST PASS MT3505 OR PASS MT4003

Anti-requisites

YOU CANNOT TAKE THIS MODULE IF YOU TAKE MT5823

Assessment pattern

2-hour written examination = 100%

Re-assessment

Oral examination = 100%

Learning and teaching methods and delivery

Weekly contact

3 lectures (x 10 weeks), 1 tutorial (x 10 weeks)

Scheduled learning hours

40

The number of compulsory student:staff contact hours over the period of the module.

Guided independent study hours

107

The number of hours that students are expected to invest in independent study over the period of the module.

Intended learning outcomes

  • Encounter the aspects of the theory of semigroups that are shared by many areas in universal algebra: free semigroups, homomorphisms, congruences, isomorphism theorems, subsemigroups, presentations, and so on
  • Develop a good understanding of the fundamental aspect of the theory that are unique to the semigroups, including Green's relations, Green's lemma, the Rees theorem
  • Learn to determine the structure of an arbitrary semigroup defined by a finite generating set
  • Develop a familiarity with several standard examples of semigroups, such as the full transformation monoids, rectangular bands, Rees 0-matrix semigroups, left and right zero semigroups, semigroups defined by presentations, and so on
  • Study several special classes of semigroup: simple, inverse, regular, or Clifford semigroups
  • Study some methods of constructing new semigroups from old via, for instance, direct products