# nLab Bézout monoid

Contents

### Context

#### Algebra

higher algebra

universal algebra

## Theorems

#### Monoid theory

monoid theory in algebra:

# Contents

## Definition

A monoid (or semigroup) $M$ is a left Bézout monoid if all finitely generated left ideals of $M$ are left principal ideals in $M$. Similarily, $M$ is a right Bézout monoid if all finitely generated right ideals of $M$ are right principal ideals. Finally, $M$ is a Bézout monoid if it is both a left Bézout monoid and a right Bézout monoid.

Last revised on May 21, 2021 at 18:26:26. See the history of this page for a list of all contributions to it.