# Definition:Null Ideal

(Redirected from Definition:Zero Ideal of Ring)

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## Definition

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

The null ring $\struct {\set {0_R}, +, \circ}$ is called the **null ideal** of $R$.

## Also known as

The **null ideal** is also known as the **zero ideal**.

## Also see

- Null Ring is Ideal: $\struct {\set {0_R}, +, \circ}$ is proved to be an ideal of $R$.

## Sources

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