prime ideal
1. Definition
Let \(R\) be a commutative ring and \(\mathfrak{p} \subsetneq R\) a strict ideal. Then \(\mathfrak{p}\) is a prime ideal, if for \(a,b \in R\) with \(a \cdot b \in R\)
\begin{align*} a \in \mathfrak{p} \lor b \in \mathfrak{p} \end{align*}