MATH40630 Ring Theory

Academic Year 2022/2023

The course introduces the basic notions on rings and modules and develops the structure theory of simple and semisimple artinian rings.
Content: Basic notions on rings and modules, Wedderburn's theorem on finite division rings, semisimple modules and rings, simple rings, the Jacobson radical. Time permitting: semisimple group rings, Maschke's theorem.

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Curricular information is subject to change

Learning Outcomes:

The student will know:
-the basic properties of rings and modules, including chain conditions and composition series,
-simple and semisimple rings and modules, including the Wedderburn-Artin structure results,
-the Jacobson radical and its links with semisimplicity.

Student Effort Hours: 
Student Effort Type Hours
Lectures

24
Practical

12
Autonomous Student Learning

90
Total

126
Approaches to Teaching and Learning:
Lectures, tutorials, enquiry and problem-based learning. 
Requirements, Exclusions and Recommendations
Learning Requirements:

Prior to taking this module, students should have completed:
1) a reasonably advanced course in linear algebra similar to (for example) MATH20300.
2) an introductory first course on groups or rings. This course should contain at least a presentation of these objects and of their first properties (subgroups or ideals, quotients, morphisms). MATH20310 is an example of such a course.

All questions about eligibility (in particular if you think the meet the requirements but have not passed MATH20300 and MATH20310) should be addressed to the module coordinator.


Module Requisites and Incompatibles
Not applicable to this module.
 
Assessment Strategy  
Description Timing Open Book Exam Component Scale Must Pass Component % of Final Grade
Examination: End of trimester exam. 2 hour End of Trimester Exam No Standard conversion grade scale 40% No

75
Examination: Mid-term exam. The timing of the midterm can be slightly changed in order to accommodate everyone. Week 7 No Standard conversion grade scale 40% No

25

Carry forward of passed components
No
 
Resit In Terminal Exam
Autumn Yes - 2 Hour
Please see Student Jargon Buster for more information about remediation types and timing. 
Feedback Strategy/Strategies

• Feedback individually to students, post-assessment
• Group/class feedback, post-assessment

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