| کلیدواژهها
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k-clean, monomial ideal, Stanley-Reisner ideal, Cohen-Macaulay,
forest type, matroid.
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| چکیده
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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 (d−1)-dimensional simplicial complex is k-decomposable if and only if its
Stanley-Reisner ideal is k-clean, where k ≤ d − 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 StanleyReisner
ideals of matroid complexes are k-clean for all k ≥ 0.
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