affine curve

《Algebraic Geometry》 · 第 4 页 · Chapter I，Example 1.4.2

Let $f$ be an irreducible polynomial in $A=k[x,y]$. Then $f$ generates a prime ideal in $A$, since $A$ is a unique factorization domain, so the zero set $Y=Z(f)$ is irreducible. We call it the affine curve defined by the equation $f(x,y)=0$.