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Definition: Divisibility of Ideals
Let $I\lhd R$ and $J\lhd R$ be two ideals of the ring $R$. Then we say that the ideal $I$ divides the ideal $J$ (or that $J$ is a multiple or that $J$ is divisible by $I$)  symbolically \(I \mid J\), if \(I\) is a superset of \( J \):
\[I \mid J\Longleftrightarrow I\supseteq J.\]
Mentioned in:
Lemmas: 1
Proofs: 2 3 4
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References
Bibliography
 Kramer Jürg, von Pippich, AnnaMaria: "Von den natürlichen Zahlen zu den Quaternionen", SpringerSpektrum, 2013