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We give a new characterization for prime filtrations of an R-module M in terms of primary decomposition of the zero submodule of M. Using this characterization we prove that some classes of monomial ideals like generic and cogeneric monomial ideals are clean, pretty clean, or almost clean.
This research was in part supported by a grant from IPM (No.87130014).
Communicated by R. Villarveal.
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