Definition:Integral Ideal

Definition
Let $J \subseteq \Z$ be a non-empty subset of the set of integers.

Let $J$ fulfil the following conditions:


 * $(1): \quad n, m \in J \implies m + n \in J, m - n \in J$


 * $(2): \quad n \in J, r \in \Z \implies r n \in J$

Then $J$ is an integral ideal.

Also see

 * Definition:Ideal of Ring, of which this is a particular instance


 * Integral Ideal is Ideal of Ring which demonstrates that fact