Grassmann algebra

A Grassmann algebra is an exterior algebra regarded as an algebra of anticommuting generators. Its odd elements satisfy ${\theta }_i{\theta }_j=-{\theta }_j{\theta }_i$.

A Grassmann variable is an odd generator $\theta$ of a Grassmann algebra. In characteristic zero it obeys ${\theta }^2=0$, so functions of finitely many Grassmann variables have finite Taylor expansions.