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

• Results about integral ideals can be found here.

Sources

• 1971: George E. Andrews: Number Theory ... (previous) ... (next): $\text {2-1}$ Euclid's Division Lemma: Exercise $4$