Week 4: nilpotents, idempotents. Subrings, Ideals,
Course Material
- Week 1: Rings: Definition, examples. Quadratic integer rings,
- Week 2:Examples of non-commutative rings,
- Week 3: The Hamilton quaternions. Polynomial rings. Matrix rings. Units, zero-divisors,
- Week 4: nilpotents, idempotents. Subrings, Ideals,
- Week 5: Maximal and prime Ideals. Left, right and two-sided ideals; Operations with ideals,
- week 6: The ideal generated by a set. Quotient rings. Ring homomorphism,
- Week 7: The isomorphism theorems, applications. Finitely generated ideals. Rings of fractions,
- Week 8: Integral Domain: The Chinese remainder theorem
- Week 9: Mid term
- Week 10:Divisibility in integral domains,
- Week 11:greatest common divisor, least common multiple
- Week 12:Euclidean domains,
- Week 13: The Euclidean algorithm,
- Week 14: Principal ideal domains,
- Week 15: Prime and irreducible elements in an integral domain
- Week 16:Gauss lemma
- Week 17:, irreducibility criteria for polynomials.
- Week 18: Final term
- Chapters 18
- Department Mathematics
- Teacher
Ms.Bushra Batool
