MATH338 - Algebra IIIB
This unit further develops the theory of algebraic structures which is first studied in MATH337, and involves the study of a selection of topics in ring theory and field theory.
The ring theory strand will develop the basic theory, including integral domains, ideals, quotient rings, principal ideal domains, unique factorization domains and Euclidean domains, followed by a study of one or two topics related to ring theory such as ideals in quadratic fields, the first case of Fermat's last theorem, Hopf algebras or the Wedderburn structure theorem.
The field theory strand will also develop the basic theory, including the notion of irreducibility, simple, algebraic and transcendental extensions, and the tower law. The ideas of group theory studied in MATH337 will then be applied to the study of field extensions via the notion of automorphisms, culminating in the study of the Galois correspondence theorem.
Prerequisites: MATH337(P).
Corequisites: None.
Not Counted for Credit With: None.