# Undergraduate Catalogue of Courses 2012/2013

## MATHEMATICAL SCIENCES

MX 3531

RINGS AND FIELDS

CREDIT POINTS 15

*Course Co-ordinator:* Dr D Quinn

*Pre-requisite(s):*
MX 3020

- 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.

2 one-hour lectures and 1 one-hour tutorial per week.

1st Attempt: 1 two-hour written examination (80%); in-course assessment (20%).

Resit: 1 two-hour examination (maximum of 100% resit and 80% resit with 20% in-course assessment).

Only the marks obtained on first sitting can be used for Honours classification.