In algebraic geometry, a finite morphism between two affine varieties X, Y {\displaystyle X,Y} is a dense regular map which induces isomorphic inclusion k [ Y ] ↪ k [ X ] {\displaystyle k\left[Y\right]\hookrightarrow k\left[X\right]} between their coordinate rings, such that k [ X ] {\displaystyle k\left[X\right]} is integral over k [ Y ] {\displaystyle k\left[Y\right]}. Wikipedia