  Primary decomposition is a very important tool of commutative algebra and
geometry. In this paper we generalized some of the existing algorithms of
primary decomposition developed by Eisenbud et al. (cf. [EHV]) for free modules
and also filled some gaps by providing proofs of important theorems(2.9, 2.12,
2.13) appeared in [EHV]. All these algorithms are programmed and implemented in
{\sc Singular}.
