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MX3531: RINGS & FIELDS (2021-2022)

Last modified: 31 May 2022 13:05

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.

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 31 August 2023 for 1st half-session courses and 22 December 2023 for 2nd half-session courses.

Summative Assessments

Alternative Assessment

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

Alternative Resit Assessment

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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