Splitting Fields

Summary . In this article we further develop field theory in Mizar [1], [2]: prove existence and uniqueness of splitting fields. We define the a polynomial p ∈ F [ X ] as smallest extension , which splits into linear factors. From follows, that for E have = ( A ) where is set ’s roots. Splitting fields are unique, however, only up to isomorphisms; be more precise -isomorphims i.e. isomorphisms i with i| Id two -isomorphic using well-known technique [4], [3] extending from 1 → 2 b being algebraic over respectively.