Definition:Ideal of Ring/Proper Ideal
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Definition
Let $\struct {R, +, \circ}$ be a ring.
A proper ideal $J$ of $\struct {R, +, \circ}$ is an ideal of $R$ such that $J$ is a proper subset of $R$.
That is, such that $J \subseteq R$ and $J \ne R$.
Sources
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {IV}$: Rings and Fields: $22$. New Rings from Old