| 释义 |
splitting field Given a polynomial f(x) with coefficients from a field F, its splitting field K is the smallest field in which f(x) factorizes into linear factors. The splitting field is unique up to isomorphism. For example, the splitting field of x2+1 over ℚ is ℚ[i] as
x2+1 = (x − i)(x+i). |