MX3531: RINGS & FIELDS (2020-2021)

Last modified: 05 Aug 2021 13:04

Course Overview

Many examples of rings will be familiar before entering this course. Examples include the integers modulo n, the complex numbers and n-by-n matrices with real entries. The course develops from the fundamental definition of ring to study particular classes of rings and how they relate to each other. We also encounter generalisations of familiar concepts, such as what is means for a polynomial to be prime.

Course Details

Study Type	Undergraduate	Level	3
Term	Second Term	Credit Points	15 credits (7.5 ECTS credits)
Campus	Aberdeen	Sustained Study	No
Co-ordinators	Dr Ehud Meir

Qualification Prerequisites

Either Programme Level 3 or Programme Level 4

What courses & programmes must have been taken before this course?

Either MA2008 Linear Algebra I (Passed) or MA2506 Linear Algebra (Passed)
Any Undergraduate Programme (Studied)
MX3020 Group Theory (Studied)

What other courses must be taken with this course?

None.

What courses cannot be taken with this course?

None.

Are there a limited number of places available?

Course Description

Basic concepts and examples. Ideals, factor rings, isomorphism theorems.
Rings of polynomials.
Field of fractions of a domain.
Unique Factorization Domains, Principal Ideal Domains, Euclidean Domains.
Passage from R to R[X]. Gauss's Theorem. Eisenstein's criterion.
Fields : characteristic, prime subfield.
Finite fields, construction.
Algebraic and transcendental elements, algebraic closure.

Syllabus

Rings
Zero divisors and integral domains.
Homomorphisms.
Ideals and quotient rings.
Field of fractions of an ID.
ID, UFD, PID and ED.
Polynomial rings over commutative rings.
Field extensions
Splitting fields.
Finite fields.

Contact Teaching Time

Information on contact teaching time is available from the course guide.

Teaching Breakdown

More Information about Week Numbers

Details, including assessments, may be subject to change until 30 August 2024 for 1st term courses and 20 December 2024 for 2nd term courses.

Summative Assessments

Three standard course assignments - 30%, 30% and 40%

Alternative Resit Arrangements for students taking course in Academic Year 2020/21

Resubmission of failed elements (pass marks carried forward)

Formative Assessment

There are no assessments for this course.

Course Learning Outcomes

Knowledge Level	Thinking Skill	Outcome

Factual	Remember	ILO’s for this course are available in the course guide.