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1. Discriminant

   Linked via "minimal polynomial"

   The Discriminant in Field Theory
   In algebraic number theory, the discriminant of a number field $K$ (or, more precisely, of an order $\mathcal{O}K$) is an essential invariant calculated from the basis elements of the ring of integers. If $K = \mathbb{Q}(\alpha)$ is an extension of degree $n$ defined by an algebraic number $\alpha$ whose minimal polynomial is $P(x) = x^n + a{n-1}x^{n-1} + \dots + a_0$, and…