Module multiplicity is a number associated with every nonzero finitely generated graded module M over a graded ring R for which the Hilbert series is defined. If dim(M) = d, the Hilbert series of M can be written in the form H_M(t) = (Q_M(t))/(1 - t)^d, and the multiplicity of M is the integer e(M) = Q_M(1).

associated graded module | multiplicity