MTH403: (Fields and Galois Theory)

        [Cr:4, Lc:3, Tt:1, Lb:0]

Course Outline

• Field extensions, algebraic extensions, Splitting Fields, Algebraic Closure.
• Separable and inseparable extensions. Normal extensions.
• Perfect fields, Finite fields.
• Automorphisms of extensions, Galois extensions and Galois group, fundamental theorem of Galois theory.
• Examples of Galois extensions over Q, abelian and cyclotomic extensions.
• Solutions of polynomial equations by radicals, constructible numbers.
• Transcendental extensions, transcendence bases.

Additional Topics Infinite Galois theory.

Reference texts:

1. S. Lang: Algebra
2. Dummit and Foote: Abstract Algebra.
3. Artin: Algebra.
4. Herstein: Topics in Algebra.