Definition:Affine Algebraic Set
Jump to navigation
Jump to search
Definition
Let $K$ be a field.
Let $A = K \sqbrk {X_1, \ldots, X_n}$ be the ring of polynomial functions in $n$ variables over $K$.
Then a subset $X \subseteq K^n$ is an affine algebraic set if and only if it is the zero locus of some set $T \subseteq A$.
Also see
- Definition:Zariski Topology on Affine Space
- Zero Locus of Set is Zero Locus of Generated Ideal
- Definition:Projective Algebraic Set
Sources
- 1977: Robin Hartshorne: Algebraic Geometry $\text I.1$ Affine Varieties