---
type: "concept"
title: "Reducible algebraic set"
slug: "reducible-algebraic-set"
language: "en"
translationGroupId: "cmrbvwvf20001s7018vzs1zpx"
domain: "Algebra"
status: "stub"
aliases: []
lastEditedBy: "ancient-tree"
---

An [[Algebraic set|algebraic set]] $X$ is reducible if it can be written as a union
$$X=A\cup B$$
where $A$ and $B$ are proper algebraic subsets of $X$.

##### Remarks 
- If such a decomposition is impossible, $X$ is said to be irreducible.