# Definition:Non-Null Ideal

(Redirected from Definition:Nonzero Ideal of Ring)

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## Definition

Let $\struct {R, +, \circ}$ be a ring whose zero is $0_R$.

Let $J$ be an ideal of $R$ such that $J \ne \set {0_R}$.

Then $J$ is a **non-null ideal** of $R$.

## Also known as

A **non-null ideal** is also known as a **non-zero ideal**.

## Also see

## Sources

- 1965: Seth Warner:
*Modern Algebra*... (previous) ... (next): Chapter $\text {IV}$: Rings and Fields: $22$. New Rings from Old