2017/02/24 by Rahim Rahmati-Asghar, Rahmati-Asghar, Rahim
Computer Science · Mathematics · #05E40 #13F55 #13P10 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Rings, Modules, and Algebras #math.AC #math.CO #msc:05E40 #msc:13F55 #msc:13P10
paper · pdf · doi:10.48550/arxiv.1702.07574
12 pages
arxiv created 2017/02/24 · openalex publication_date 2017/02/24 · arxiv updated 2017/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 monomial complete intersection ideals, Cohen-Macaulay monomial ideals of codimension 2 and symbolic powers of Stanley-Reisner ideals of matroid complexes are k-clean for all k≥ 0.