MAT 322E - Algebra

Course Objectives

1- To teach groups and group theory.
2- To teach rings and ring theory.
3- To show the relations between rings and fields.

Course Description

Introduction; arithmetic on integers, equivalence relations, functions.
Groups; group axioms, subgroup, normal subgroup, Langrange’s theorem, homomorphisms,
Cayley’s theorem, permutation groups, conjugacy classes, the class equation of a group, the
structure of Abelian groups.
Rings; rings and ideals, polynomial rings, quotient rings, homomorphisms, rational field, unique
factorization theorem, principle ideal domain, Euclidean domain, prime and maximal ideals,
unique factorization over polynomial rings.