Definition 2

Let A be a noetherian ring, q an ideal of A contained in the radical of A, and M a finitely generated A-module such that $M/qM$ is of finite length. An element x of A is said to be superficial for M relative to q if it belongs to q and if, for every $n$ sufficiently large, the mapping $q^n M/q^{n+1} M \to q^{n+1} M/q^{n+2} M$ induced by multiplication by x is injective.