# Definition:Principal Ideal Domain

## Contents

## Definition

A **principal ideal domain** is an integral domain in which every ideal is a principal ideal.

## Also known as

Another term seen for **principal ideal domain** is **principal ideal ring**.

## Also see

- Results about
**principal ideal domains**can be found here.

## Sources

- 1972: A.G. Howson:
*A Handbook of Terms used in Algebra and Analysis*... (previous) ... (next): $\S 6$: Rings and fields - 1978: Thomas A. Whitelaw:
*An Introduction to Abstract Algebra*... (previous) ... (next): $\S 59$. Principal ideals in a commutative ring with a one