### Abstract

This entry provides a type class for

*perfect fields*. A perfect field*K*can be characterized by one of the following equivalent conditions:- Any irreducible polynomial
*p*is separable, i.e.*gcd(p,p') = 1*, or, equivalently,*p'*non-zero. - Either the characteristic of
*K*is 0 or*p > 0*and the Frobenius endomorphism is surjective (i.e. every element of*K*has a*p*-th root).

- any field of characteristic 0 (e.g. the reals or complex numbers)
- any finite field (i.e.
*F*for_{q}*q=p*,^{n}*n > 0*and*p*prime) - any algebraically closed field (for example the formal Puiseux series over finite fields)