# Definition:Ideal of Ring/Proper Ideal

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## Definition

Let $\left({R, +, \circ}\right)$ be a ring.

A proper ideal $J$ of $\left({R, +, \circ}\right)$ is an ideal of $R$ such that $J$ is a proper subset of $R$.

That is, such that $J \subseteq R$ and $J \ne R$.