Past exam of the mathematics course of the University of Cambridge / 2020 / ii / Paper 1 / 18G / b / i

A splitting field of $f\in K[X]$ is an extension $L/K$ in whichfor roots ${\alpha }_r\in L$, and which is generated by those roots:The generation condition is the required minimality: no proper intermediate field containing $K$ can still contain every root.