Course Description
Rings and fields, integral domains, characteristic, the field of quotients of an integral domain, rings of polynomials, factorization of polynomials over a field. Homomorphisms and factor rings, prime and maximal ideals. Unique factorization domains, Euclidian domains, Gaussian integers
Course Objectives & Outcomes
Objectives:
- Define rings, field and ideals.
- Define polynomial over a field.
- Equip students with necessary knowledge and skills to enable them handle quotient ring, unique factorization domains and Euclidian domains
Outcomes: Upon successful completion of this course, the student will be able to:
- Characterize rings, fields, and integral domain.
- Define the field of quotients of an integral domain.
- Recognize rings of polynomials and factorization of polynomials over fields.
- Identify homomorphisms and quotient rings.
- Characterize prime and maximal ideals.
- Identify unique factorization of domains.
- Recognize Euclidean domains.
References
1.Fraleigh,J.B.(2003)A First Course in Abstract Algebra,7th Edition, Pearson, ISBN-10: 0201763907,ISBN-13: 978-0201763904.
2. Gallian,J.(2012) Contemporary Abstract Algebra, 8th Edition, Cengage Learning, ISBN-1285402731, 9781285402734.
3.Cohn,P. M.(2003) Basic Algebra:Groups, Rings and Fields, Springer, ISBN: 978-1-4471-1060-6 (Print) ,978-0-85729-428-9 (Online).
Course ID: MATH 407
Credit hours | Theory | Practical | Laboratory | Lecture | Studio | Contact hours | Pre-requisite | 3 | 3 | 3 | Principle of Algebra |
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