By the very definition of a perfect field, Theorem 3.1.6 implies that the following properties are equivalent: a) K is a perfect field; b) any irreducible polynomial of K[X] is separable; c) any element of an algebraic closure of K is separable over K; d) any algebraic extension of K is separable; e) for any finite extension K→L, the number of K-homomrphisms from K to an algebraically closed extension of K is equal to [L:K]. Corollary 3.1.8. Any algebraic extension of a perfect field is again a perfect field.

I gave him the charge to get the deal closed by the end of the month.

Someone is liable to slip on your icy sidewalk.

The idea of an absolute majority is somewhat ambiguous, sometimes simply meaning a majority of the vote total and sometimes a majority of all eligible voters.