# Affine Varieties - the x-axis in R^2

#### Peter

##### Well-known member
MHB Site Helper
In Dummit and Foote, Chapter 15, Section 15.2 Radicals and Affine Varieties, Example 2, page 681 begins as follows:

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"The x-axis in $$\displaystyle \mathbb{R}^2$$ is irreducible since it has coordinate ring

$$\displaystyle \mathbb{R}[x,y]/(y) \cong \mathbb{R}[x]$$

which is an integral domain."

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$$\displaystyle \mathbb{R}[x,y]/(y) \cong \mathbb{R}[x]$$ is established.