Definition:Affine Algebraic Variety/Definition 2

Definition

Let $k$ be a field.

Let $n \ge 1$ be an Integer.

An affine algebraic variety in $k^n$ is a subset defined by polynomial equations in $x_1, x_2, \ldots, x_n$.

Also known as

An affine algebraic variety is also called an affine variety.

Also see

• Equivalence of Definitions of Affine Algebraic Variety

• Results about affine algebraic varieties can be found here.

Sources

• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): affine variety
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): variety