A separable extension K of a field F is one in which every element's algebraic number minimal polynomial does not have multiple roots. In other words, the minimal polynomial of any element is a separable polynomial. For example, Q(sqrt(2)) = {a + bsqrt(2):a, b element Q} is a separable extension since the minimal polynomial of a + bsqrt(2), when b!=0, is x^2 - 2a x + a^2 - 2b^2 = (x - a + bsqrt(2))(x - a - bsqrt(2)).

algebraic number minimal polynomial | extension field | multiple root | purely inseparable extension | separable graph | separable morphism | separable polynomial | separable space