NONCOMMUTATIVE ALGEBRA - 2020/1
Module code: MATM049
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This module extends students’ knowledge of ring theory and introduces various topics in noncommutative algebra.
FISHER David (Maths)
Number of Credits: 15
ECTS Credits: 7.5
Framework: FHEQ Level 7
JACs code: G100
Module cap (Maximum number of students): N/A
Prerequisites / Co-requisites
MAT2048 Groups and Rings
Indicative content includes:
Lie algebras, subalgebras, ideals, quotient algebras and direct sums.
Derivations, homomorphisms and automorphisms of algebras.
Modules over rings; vector spaces over division rings.
Noetherian and Artinian rings.
Wedderburn's decomposition theorem.
Nilpotency, solvability and semisimplicity.
Tensor products of rings and modules. Application to algebra automorphisms.
|Assessment type||Unit of assessment||Weighting|
|School-timetabled exam/test||IN-SEMESTER TEST (50 MINS)||20|
|Examination||EXAMINATION (2 HOURS)||80|
The assessment strategy is designed to provide students with the opportunity to demonstrate their ability to
construct and interpret mathematical arguments in the context of this module;
display subject knowledge by recalling key definitions and results;
apply the techniques learnt to both routine and unfamiliar problems.
Thus, the summative assessment for this module consists of:
One two-hour examination at the end of Semester 2, worth 80% of the module mark.
In-semester test, worth 20% of the module mark
Formative assessment and feedback
Students receive written comments on their marked test and assignments. Verbal feedback is provided in lectures and office hours.
- enhance students' appreciation of abstract algebraic structure theory,
- develop an understanding of noncommutative ring theory and modules over rings,
- provide a foundation for independent study of algebraic topics.
|001||Know the definitions and language associated with rings, algebras and modules and be familiar with examples||K|
|002||Appreciate the relationships between the structures studied in this module and those encountered in previous algebraic modules||KCT|
|003||Know and be able to apply a variety of standard results and structure theorems, as listed in the module content||KC|
|004||Devise solutions of algebraic problems involving the concepts studied||KC|
|005||Read and interpret varying presentations of the material||CT|
|006||Construct simple proofs similar to those encountered in the module||KCT|
C - Cognitive/analytical
K - Subject knowledge
T - Transferable skills
P - Professional/Practical skills
Overall student workload
Independent Study Hours: 117
Lecture Hours: 33
Methods of Teaching / Learning
The learning and teaching strategy is designed to provide:
An enhanced awareness of the theory and applications of abstract algebra
Experience of the methods used to interpret, understand and solve problems in the topics covered.
The learning and teaching methods include:
Three 50-minute lectures per week for eleven weeks, some being used as tutorials, problem classes and a test.
Online notes supplemented by additional examples in lectures.
Unassessed coursework consisting of exercises from the notes.
- Personal assistance given to individuals and small groups in office hours.
Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.
Upon accessing the reading list, please search for the module using the module code: MATM049
Programmes this module appears in
|Mathematics MSc||2||Optional||A weighted aggregate mark of 50% is required to pass the module|
Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2020/1 academic year.