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Abstract: We show that an arbitrary monomial ideal I is pretty clean if and only if its polarization is clean. This yields a new characterization of pretty clean monomial ideals in terms of the arithmetic degree, and it also implies that a multicomplex is shellable if and only the simplicial complex corresponding to its polarization is (non-pure) shellable. We also discuss Stanley decompositions in relation to prime filtrations. [Copyright &y& Elsevier]