چکیده
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We introduce pretty k-clean monomial ideals and k-decomposable multicomplexes,
respectively, as the extensions of the notions of k-clean monomial ideals
and k-decomposable simplicial complexes. We show that a multicomplex Γ is kdecomposable
if and only if its associated monomial ideal I(Γ) is pretty k-clean.
Also, we prove that an arbitrary monomial ideal I is pretty k-clean if and only
if its polarization Ip is k-clean. Our results extend and generalize some results
due to Herzog-Popescu, Soleyman Jahan and the first author
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