|
tutorial |
Lecture |
credit |
Subject |
Week |
|
1 |
1 |
1 |
Rings (definitions, elementary concepts, and basic properties) |
1 |
|
1 |
2 |
2 |
Special types of rings |
1 |
|
1 |
2 |
3 |
Elements of ring such as idempotent elements - nilpotent elements- invertible elements- zero divisors |
2 |
|
1 |
2 |
3 |
Subring and its properties- Integral domain and its properties |
3 |
|
1 |
2 |
3 |
Fields: (definitions, and basic properties) and the relationship between the integral domain and the field
|
4 |
|
|
|
|
First midterm exam (2 hours) |
5 |
|
1 |
3 |
4 |
Characteristic of ring and the field - The Ideals and its properties - principal Ideal |
5-6 |
|
1 |
2 |
3 |
Quotient ring and its properties - Homomorphism of rings and its properties. |
7 |
|
1 |
2 |
3 |
Study the effect of conformation on subrings and ideals |
8 |
|
1 |
2 |
3 |
The Kernal of homomorphism and its properties |
9 |
|
1 |
2 |
3 |
Kernal of homomorphism and its properties |
10 |
|
|
|
|
Second midterm exam (2 hours) |
11 |
|
1 |
2 |
3 |
The first theory in the Isomorphism of rings, its application, and building a field from an integral domain |
12 |
|
1 |
2 |
3 |
prime ideals and their properties in commutative rings, |
13 |
|
2 |
4 |
6 |
Studying some important rings, such as the principal ideals ring and the polynomial ring |
14 |
|
|
|
|
|
|
|
|
|
|
Final exam |
|
|
|
|
42 |
Total |
|
References
|
References Title |
Publisher |
Version |
Author |
|
First Course in Abstract Algebra |
Publications Management |
1998 |
John B. Farleigh |