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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.

Course Coordinator
Ergün Yaraneri
Course Language
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