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DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Topics in Noncommutative Algebra (MATH11143)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 11 (Year 5 Undergraduate) AvailabilityAvailable to all students
SCQF Credits10 ECTS Credits5
SummaryWhile 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.
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) AND Introduction to Number Theory (MATH10071)
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-requisitesVisiting 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? Yes
Course Delivery Information
Academic year 2023/24, 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 90 %, Coursework 10 %, Practical Exam 0 %
Additional Information (Assessment) Coursework 10%, Examination 90%

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Exam Information
Exam Diet Paper Name Hours & Minutes
Main Exam Diet S1 (December)Topics in Noncommutative Algebra (MATH11143)2:00
Learning Outcomes
On completion of this course, the student will be able to:
  1. become fluent working with rings.
  2. use the structure theorems of finite dimensional algebras to solve problems in ring theory.
  3. state important theorems in noncommutative algebra and explain key steeps in their proof.
  4. solve unseen problems in noncommutative algebras.
  5. 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
Course organiserDr Agata Smoktunowicz
Course secretaryMr Martin Delaney
Tel: (0131 6)50 6427
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