Ideals: Polynomials and Definitions

This lecture covers the concept of ideals in K[X], starting with the definition of the greatest common divisor (PGCD) of polynomials. It explains the properties of PGCD, uniqueness, and its relation to being coprime. The lecture then introduces the definition of an ideal as a non-empty subset of K[X] satisfying specific conditions. It discusses the existence of a polynomial M for any ideal I, leading to the concept of MP,Q as an ideal generated by two polynomials. The lecture concludes with the theorems of Bézout and Gauss, highlighting the relationships between polynomials, ideals, and divisibility.