MATH 322

Course Code & Number

MATH 322

Course Title

Abstract Algebra II

Level

BS

Credit Hours/ ECTS Credits

(3+1+0) 3 TEDU Credits, 7 ECTS Credits

Year of Study:

Junior

Semester:

Spring

Type of Course:

Compulsory

Mode of Delivery:

Face-to-face

Language of Instruction:

English

Pre-requisite / Co-requisite::

Catalog Description

Rings. Subrings. Integral domains and fields. Isomorphisms and homomorphisms. Ideals and quotient rings. Polynomial rings. Euclidean Domains. Principal Ideal Domains. Unique Factorization Domains. The field of quotients of an integral domain. Field extensions. Splitting fields. Finite fields.

Course Objectives

The main objective of this course is to provide a comprehensive understanding of ring and field theory, extending foundational algebraic concepts to more complex structures and fostering the mathematical rigor required for advanced algebraic analysis. 

Course Learning Outcomes

Upon completion of this course, students will be able to: 

1. Identify rings, subrings, integral domains, and fields using their defining and structural properties, 
2. Analyze ring homomorphisms, isomorphisms, ideals, and quotient rings using fundamental mapping properties and the Isomorphism Theorems, 
3. Investigate divisibility, irreducibility, and factorization across polynomial rings and integral domains, including Euclidean domains, principal ideal domains, and unique factorization domains, 
4. Analyze the structure and properties of field extensions through their basis, degree, algebraic or transcendental classification, splitting fields, finite fields, and polynomial separability, 
5. Construct rigorous mathematical proofs of algebraic statements and results in ring and field theory. 

Course Coordinator:

Dr. Fuat Erdem