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