Definition:Affine Algebraic Variety
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Definition
Let $k$ be a field.
Let $n \ge 1$ be an Integer.
Then a subset $X \subseteq k^n$ is an affine algebraic variety if the following hold:
- $(1): \quad X$ is an affine algebraic set
- $(2): \quad X$ is irreducible with respect to the Zariski topology.
Also known as
This is also called affine variety.
Also see
Sources
- 1977: Robin Hartshorne: Algebraic Geometry $\text{I}.1$ Affine Varieties