---
type: "concept"
title: "Algebraic set"
slug: "algebraic-set"
language: "en"
translationGroupId: "cmrbs3wxm0009pa012ct89wwm"
domain: "Algebra"
status: "stub"
aliases: []
lastEditedBy: "ancient-tree"
---

A subset $X$ of an [[Affine space over a field|affine space]] $\mathbb{A}^{n}_{k}$ is called an algebraic set if there exists a set $S$ of polynomials whose [[Zero locus|zero locus]] is $X$:
$$X=V(S).$$