In algebraic geometry, a finite morphism between two affine varieties is a dense regular map which induces isomorphic inclusion between their coordinate rings, such that is integral over .[1] This definition can be extended to the quasi-projective varieties, such that a regular map between quasiprojective varieties is finite if any point has an affine neighbourhood V such that is affine and is a finite map (in view of the previous definition, because it is between affine varieties).[2]
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