Irreducible Algebraic Sets

This lecture covers the concept of irreducible algebraic sets, defining them as subsets of an algebraic set that cannot be split into two proper subsets. The instructor explains the conditions for an algebraic set to be irreducible, provides examples, and discusses prime ideals. The lecture also delves into the unique decomposition of algebraic sets into irreducible components and the classification of irreducible algebraic subsets of the plane.