Changes

<math>p \in \mathbb{Z}  \quad prime :\Leftrightarrow p \not\in \{-1, 1\} \wedge (\forall a,b \in \mathbb{Z}: p \vert ab \Rightarrow p \vert a \vee p \vert b) </math>

<math>p \in \mathbb{Z}  \quad prime :\Leftrightarrow p \not\in \{-1, 1\} \wedge (\forall a,b \in \mathbb{Z}: p \vert ab \Rightarrow p \vert a \vee p \vert b) </math>

The advantage of this formulation is that it can be generalized on other structures which allow for addition and multiplication, i.e., [[ring]]s. The earlier definition involves the notion of [[irreducibility]].

The advantage of this formulation is that it can be generalized on other structures which allow for addition and multiplication, i.e., [[Ring_(mathematics)|ring]]s. The earlier definition involves the notion of [[irreducibility]].

==Unique Factorization==

==Unique Factorization==