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  NB. This course is delivered *biennially* with the next instance being in 202324. 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 infinitedimensional noncommutative associative rings, including the ArtinWedderburn theorem and applications of nilpotent rings to the YangBaxter equation. 
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)
Prerequisites 
Students MUST have passed:
Honours Algebra (MATH10069) AND
Introduction to Number Theory (MATH10071)

Corequisites  
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
Prerequisites  Visiting students are advised to check that they have studied the material covered in the syllabus of any prerequisite course listed above before enrolling 
High Demand Course? 
Yes 
Course Delivery Information
Not being delivered 
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 steeps 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 SpringerVerlag 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 

