MTH308: (Rings and Modules)

        [Cr:4, Lc:3, Tt:1, Lb:0]

Course Outline

• Definitions and examples of commutative and noncommutative rings, integral domains, division rings and fields.
• Ideals, maximal and prime ideals, quotients.
• Homomorphisms and isomorphisms of rings.
• Factorization in domains, Euclidean domains, principal ideal domains, unique factorization domains.
• Modules, direct sums, free modules.
• Quotients and homomorphisms of modules.
• Semisimple modules, Artinian modules, Noetherian modules, Jordan Holder theorem.
• Modules over principal ideal domains.
• Jordan decomposition of a linear transformation.
• Rational and Jordan canonical forms of matrices.

Additional Topic Artin-Wedderburn theorem, Jacobson density theorem.

Reference texts:

1. Artin: Algebra
2. Dummit and Foote: Abstract Algebra.
3. Herstein: Topics in Algebra.
4. Jacobson: Basic Algebra Vol. I
5. Hungerford: Algebra