Consider the following ring R which is the quotient of a tensor algebra generated by elements x_i in degree 1 with the relation x_ix_j=-x_jx_i when i doesn't equal j. In other words, (x_i)^2 does not equal to zero. Has anyone studied this graded ring? Does this graded ring have finite homological dimension? Is there a proof of Hilbert's szy. theorem that can be doctored to apply to it?