Definition:Integral Ideal

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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

  • Results about integral ideals can be found here.