# Get an algebra that allows generators being of degree zero?

In sage, using 'letterplaceâ€™ can get free algebra with homogenous degrees but the degree of the generators of the algebra have to be positive degree. Is there any code that I can get an algebra that allows generators of degree zero?

Welcome to Ask Sage! Thank you for your question!

I guess the simple reason for an implementation to allow only generators of positive degree is to ensure finite-dimensional graded components, so that many problems become amenable to computation. What exactly do you want to do with your algebra (which would have infinite-dimensional graded parts)?

Thanks for your reply. In fact, in my case, it is a differential grade algebra, which I would like to use sage to compute the cohomology. This dga has degree-zero generators, say x_i (finitely many), and some generators in degree one. The degree-zero generators satisfy x_i^2=x_i. So it is of finite type.