Ring theory
4 points * First semester * Clayton * Prerequisites: MAT2020 and one second-year MAP subject
Objectives On the completion of this subject students will have a basic understanding of the integers and their algebra; be able to utilise this understanding for exploring cognate algebraic structures such as rational numbers and polynomials and to gain insight into their behaviour; examine the concepts of primality and irreducibility and their mutual relationship; identify rings occurring in computer theory and applications; appreciate the role of rings both in history and in post modern civilisation.
Synopsis Rings, integral domains, group rings, the quaternions, field of quotients, quotient rings, ideals, homomorphisms, rings of polynomials, principal ideal domains, unique factorisation domains, Euclidean domains.
Assessment Examinations (1.5 hours): 70% * Assignments: 30%
Recommended texts
Fraleigh J B A first course in abstract algebra Addison-Wesley, 1994
Stillwell J C Elements of algebra Springer Verlag, 1994
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