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MX3531: RINGS & FIELDS (2021-2022)

Last modified: 20 Oct 2021 14:45

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
Session Second Sub Session Credit Points 15 credits (7.5 ECTS credits)
Campus Aberdeen Sustained Study No
  • Dr Simona Paoli

Qualification Prerequisites

  • Either Programme Level 3 or Programme Level 4

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

What other courses must be taken with this course?


What courses cannot be taken with this course?


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.


  • 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.

In light of Covid-19 this information is indicative and may be subject to change.

Contact Teaching Time

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

Teaching Breakdown

  • 2 Lectures during University weeks 26 - 30, 32 - 35, 39 - 40
  • 1 Tutorial during University weeks 27 - 30, 32 - 35, 39 - 40

More Information about Week Numbers

In light of Covid-19 and the move to blended learning delivery the assessment information advertised for second half-session courses may be subject to change. All updates for second-half session courses will be actioned in advance of the second half-session teaching starting. Please check back regularly for updates.

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 LevelThinking SkillOutcome
FactualRememberILO’s for this course are available in the course guide.

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