I am reading the webpage to learn how to determine the dimension of the solution set of a set of polynomial equations. For the first case (the commutative polynomials), it is mentioned that if it is affine polynomials, one uses the Krull dimension or trancendance degree. However, the non-affine case is not introduced, and I am very interested in this case, especially multivariate quadratic polynomial equations.
Could anyone help? Thanks a lot!