Undergraduate Course: Topics in Noncommutative Algebra (MATH11143)
|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
|Summary||NB. This course is delivered *biennially* with the next instance being in 2018-19. It is anticipated that it would then be delivered every other session thereafter.
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.
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)
|| Students MUST have passed:
Honours Algebra (MATH10069)
||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||Visiting students are advised to check that they have studied the material covered in the syllabus of any pre-requisite course listed above before enrolling
|High Demand Course?
Course Delivery Information
|Not being delivered|
On completion of this course, the student will be able to:
- The main aim of this course is for you to became fluent working with rings.
- To know the structure theorems of finite dimensional algebras.
- State important theorems in noncommutative algebra and explain key steps in their proof.
- Demonstrate comprehension by solving unseen problems in noncommutative algebra.
- Provide examples of several different kinds of noncommutative algebras.
|We will use some chapters (mainly chapter 2) from the following book: |
1. M. Bresar, Introduction to noncommutative algebra, 2014. Library: online access
The following books are recommended for enthusiasts:
2. T.Y. Lam, A first course in noncommutative rings, 2001 or 1999. Library: QA251.4 Lam
3. I.N. Herstein, Noncommutative rings, 2005. Library: online access
|Graduate Attributes and Skills
|Course organiser||Dr Agata Smoktunowicz
|Course secretary||Mr Martin Delaney
Tel: (0131 6)50 6427