Polynomial Factorization and Decomposition

This lecture covers the concepts of polynomial factorization, irreducible polynomials, ideal decomposition, and the generation of ideals. It explains the conditions for a polynomial to be irreducible, the role of the greatest common divisor, and the theorem of Bézout. The lecture also delves into the factorization of polynomials into irreducible components and the uniqueness of this factorization. Various examples and exercises are provided to illustrate these concepts.