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 2022-23. 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.
For 2020/21 the topic of this course is planned to be the structure of finite- and infinite-dimensional noncommutative associative rings, including the Artin-Wedderburn theorem and applications of¿ nilpotent¿ rings to the Yang-Baxter equation.
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) AND
Introduction to Number Theory (MATH10071)
||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:
- 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 steeps in their proof.
- solve unseen problems in noncommutative algebras.
- Provide examples of several different kinds of noncommutative algebras.
|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).
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.
|Graduate Attributes and Skills
|Course organiser||Dr Agata Smoktunowicz
|Course secretary||Mr Martin Delaney
Tel: (0131 6)50 6427