Def. Zero divisor in a ring.
Thm: If R/I contains a nonzero divisor r of degree k, then one can write down the Hilbert series and polynomial of R/(I +
Ex. If r,s are of degree A and B in C[x_1..x_n], then r is automatically a nonzero divisor, but s might be a zero divisor in R/< r >. If it's not, then the Hilbert series is 1/(1-t)^n * (1-t^A) * (1-t^B).
(Remember a HW problem that asked for a Hilbert series that looked like that?)
