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Paper   IPM / M / 15557
School of Mathematics
  Title:   K-clean monomial ideals
  Author(s):  Rahim Rahmati Asghar
  Status:   Published
  Journal: Math. Reports
  Vol.:  20
  Year:  2018
  Pages:   371-387
  Supported by:  IPM
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 Stanley- Reisner ideals of matroid complexes are k-clean for all k  0.

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