Consider vector space with coordinates x1, ... xn. Consider polynomial deRham complex (also known as Koszul complex) which is generated by xi and dx_i. As an algebra it is just $C[x_i]\otimes \Lambda ...
What are the derivations of the algebra of continuous functions on a topological manifold? A supermanifold is a locally ringed space (X,O) whose underlying space is a smooth manifold X, and whose ...