# nLab irreducible element

Contents

### Context

#### Algebra

higher algebra

universal algebra

## Theorems

#### Monoid theory

monoid theory in algebra:

# Contents

## Definition

In a monoid, an element $x$ is irreducible if it is neither invertible nor the product of two non-invertible elements. Without bias, we can say that $x$ is irreducible if, whenever it is written as a product of a finite list of elements, at least one element in the list is invertible.

Last revised on May 21, 2021 at 18:27:28. See the history of this page for a list of all contributions to it.