Purely Inseparable Decompositions

This lecture covers the concept of purely inseparable decompositions, where an element is purely inseparable if its minimal polynomial is of the form x^p - a for some prime p. It also discusses inseparable extensions, separable extensions, and algebraic closures. The instructor explains the Galois property, which characterizes separable extensions, and introduces the notion of algebraic fences in the context of algebraic closures.