Let R be a commutative ring with identity and let M be an R-module. Then M is called a multiplication module if for every submodule N of M there exists an ideal I of R such that N = 1M. Let M be a non-zero multiplication R-module. Then we prove the following: (1) there exists a bijection: N(M)$igcap$V(ann$\_{R}$(M))$ ightarrow$Spec$\_{R}$(M) and in particular, there exists a bijection: N(M)$igcap$Max(R)$ ightarrow$Max$\_{R}$(M), (2) N(M) $igcap$ V(ann$\_{R}$(M)) = Supp(M) $igcap$ V(ann$\_{R}$(M)), and (3) for every ideal I of R, The ideal $ heta$(M) = $sum$$\_{m(Rm :R M) of R has proved useful in studying multiplication modules. We generalize this ideal to prove the following result: Let R be a commutative ring with identity, P $in$ Spec(R), and M a non-zero R-module satisfying (1) M is a finitely generated multiplication module, (2) PM is a multiplication module, and (3) P$^{n}$M$ eq$P$^{n+1}$ for every positive integer n, then $igcap$$^{$\_{n=1}$(P$^{n}$ + ann$\_{R}$(M)) $in$ V(ann$\_{R}$(M)) = Supp(M) $subseteq$ N(M).