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Semigroup Theory - MAT00050M

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• Department: Mathematics
• Module co-ordinator: Dr. Brent Everitt
• Credit value: 10 credits
• Credit level: M
• Academic year of delivery: 2022-23
  • See module specification for other years: 2021-22

Related modules

Additional information

Pre-requisite knowledge for MSc students: familiarity with and maturity in handling sets, functions, algebraic structures such as groups, rings and fields; knowledge of ideals and notions of divisibility in rings.

Module will run

Occurrence	Teaching period
A	Autumn Term 2022-23

Module aims

• To familiarise students with the elementary notions of semigroup theory.

• To illustrate abstract ideas by applying them to a range of concrete examples of semigroups.

• 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 be able to handle the algebra of semigroups in a comfortable way.

• The role of structure theorems, and be able to use Rees' theorem for completely 0-simple semigroups.

• Have an appreciation of the place of semigroup theory in mathematics.

Module content

Syllabus

• Examples of semigroups and monoids.

• Semigroups, ideals, homomorphisms and congruences.

• The essential difference between semigroups and previously studied algebraic structures.

• Green's relations, regular D-classes, Green's theorem that any H-class containing an idempotent is a subgroup.

• Completely 0-simple semigroups; Rees' theorem.

• Regular and inverse semigroups.

Assessment

Task	Length	% of module mark
Closed/in-person Exam (Centrally scheduled) Semigroup Theory	2 hours	100

Special assessment rules

None

Reassessment

Task	Length	% of module mark
Closed/in-person Exam (Centrally scheduled) Semigroup Theory	2 hours	100

Module feedback

Current Department policy on feedback is available in the student handbook. Coursework and examinations will be marked and returned in accordance with this policy.

Indicative reading

J M Howie, Fundamentals of Semigroup Theory, Oxford: Clarendon Press (S 2.86 HOW)