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In [10, 11] the concept of modules satisfying dccr was introduced and developed. In this note the prime (resp. weakly prime) submodules of this class of modules is characterized. Furthermore, we prove that for a weak multiplication module which satisfies dccr, the sets of maximal and prime submodule are the same and all maximal submodules are of the form mM (= M) where m is a maximal ideal of R.