Algebra IV


Syllabus (Field Theory): Finite Fields. Field extensions, degree of a field extension. Ruler and compass constructions. Algebraic closure of a field. Transcendental bases. Galois theory in characteristic zero, Kummer extensions, cyclotomic extensions, impossibility of solving quintic equations. Time permitting: Galois theory in positive characteristic (separability, normality), Separable degree of an extension

Reference Texts:

1. M. Artin: Algebra
2. S. D. Dummit and M. R. Foote: Abstract Algebra
3. I. N. Herstein: Topics in Algebra
4. K. Hoffman and R. Kunze: Linear Algebra

https://www.isibang.ac.in/~adean/infsys/database/Bmath/Alg4.html