Weil Algebra over a Field

A Weil algebra $W$ over a Field $k$ is a (Commutative, Unital) Augmented Algebra such that:

• The underlying Vector Space is Finite Dimensional
• All elements of the Augmentation Ideal are Nilpotent.

The idea behind this is that $W$ behaves like an infinitesimally thickened version of $k$.

References

• https://ncatlab.org/nlab/show/infinitesimally+thickened+point