Undergraduate Course: Topics in Noncommutative Algebra (MATH11143)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 11 (Year 5 Undergraduate) |
Availability | Available to all students |
| SCQF Credits | 10 |
ECTS Credits | 5 |
| Summary | While commutative algebra captures and generalizes the essential properties of numbers and functions, noncommutative algebra enters naturally when studying collections of transformations and operators in diverse contexts throughout mathematics, physics and beyond. Students will learn some of the many methods and techniques in noncommutative algebra, highlighting interesting examples, key constructions, and important special classes of noncommutative algebras and their actions on linear spaces.
For 2025/26 the topic of this course will be representation theory of finite groups. |
| Course description |
The syllabus will vary from year to year. Possible topics include:
- Artinian rings
- Noncommutative noetherian rings
- Category theory
- Growth of groups and algebras
- Radicals of rings and algebras
|
Entry Requirements (not applicable to Visiting Students)
| Pre-requisites |
Students MUST have passed:
Honours Algebra (MATH10069)
|
Co-requisites | |
| Prohibited Combinations | |
Other requirements | This course is designed so as to be independent of MATH11143 Topics in Ring and Representation Theory, so that students may take either course, or both. |
Information for Visiting Students
| Pre-requisites | This is a Year 4/5 advanced, Honours level course. Visiting students are expected to have an academic profile equivalent to at least the first three years of the BSc (Hons) Mathematics programme (UTMATHB), and should be confident that their background has equipped them to undertake a course at this level. Students should have passed courses equivalent to Honours Algebra (MATH10069). |
| High Demand Course? |
Yes |
Course Delivery Information
|
| Academic year 2025/26, Available to all students (SV1)
|
Quota: None |
| Course Start |
Semester 1 |
Timetable |
Timetable |
| Learning and Teaching activities (Further Info) |
Total Hours:
100
(
Lecture Hours 22,
Seminar/Tutorial Hours 5,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
69 )
|
| Assessment (Further Info) |
Written Exam
100 %,
Coursework
0 %,
Practical Exam
0 %
|
| Additional Information (Assessment) |
Coursework 0%, Examination 100%
|
| Feedback |
Not entered |
| Exam Information |
| Exam Diet |
Paper Name |
Minutes |
|
| Main Exam Diet S1 (December) | Topics in Noncommutative Algebra (MATH11143) | 00 | |
Learning Outcomes
On completion of this course, the student will be able to:
- become fluent working with rings.
- use the structure theorems of finite dimensional algebras to solve problems in ring theory.
- state important theorems in noncommutative algebra and explain key steps in their proof.
- solve unseen problems in noncommutative algebras.
- Provide examples of several different kinds of noncommutative algebras.
|
Reading List
Introduction to Noncommutative algebra, by Matej Bre¿sar, 2014 Universitex. Library: online access (mainly chapter 2 )
Noncommutative Rings, by I. N. Herstein, 2014. Library: online access (chapters 1 and 2).
For enthusiasts:
A first Course in Noncommutative Rings, by T. Y. Lam, 2001 Springer-Verlag 2013. Library: QA251.4 Lam (chapters 1, 2, 4, 5 ).
Exercises in Classical Ring Theory, by T.Y. Lam, 2003 Springer. Library: QA247 Lam. This book contains solutions to all of the exercises from the book mentioned above, A first course in noncommutative rings. |
Additional Information
| Graduate Attributes and Skills |
Not entered |
| Keywords | TNA |
Contacts
| Course organiser | Dr Agata Smoktunowicz
Tel:
Email: A.Smoktunowicz@ed.ac.uk |
Course secretary | Mr Martin Delaney
Tel: (0131 6)50 6427
Email: Martin.Delaney@ed.ac.uk |
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