# Definition:Two Ring

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*This page is about a ring with two elements. For other uses, see Definition:Two.*

## Contents

## Definition

Let $\left({\Z_2, +_2, \times_2}\right)$ be the ring of integers modulo $2$.

Then $\left({\Z_2, +_2, \times_2}\right)$ is referred to as the **two ring**.

## Also known as

The **two ring** is also called the **ring with two elements** or the **two-element ring**.

When the context is clear, the **two ring** can be, and often is, referred to as **the two** or just **two**.

In compliance with this, it is often simply denoted $2$ or $\mathbf 2$, if no confusion can arise.

## Also see

## Sources

- 2008: Paul Halmos and Steven Givant:
*Introduction to Boolean Algebras*... (previous) ... (next): $\S 1$