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In this paper, we introduce the concept of k-clean monomial ideals as an extension of clean monomial ideals and present some homological and combinatorial properties of them. Using the hierarchal structure of k-clean ideals, we show that a (dô1)-dimensional simplicial complex is k-decomposable if and only if its Stanley-Reisner ideal is k-clean, where k d ô 1. We prove that the classes of monomial ideals like Cohen-Macaulay ideals of codimension 2, monomial ideals of forest type without embedded prime ideal and symbolic powers of Stanley- Reisner ideals of matroid complexes are k-clean for all k 0.
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