2017/03/16 by Rahim Rahmati-Asghar, Rahmati-Asghar, Rahim
Mathematics · #13C14 #16W70 #Algebraic structures and combinatorial models #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Primary 13C13 #Rings, Modules, and Algebras #Secondary 05E99
paper · pdf · doi:10.48550/arxiv.1703.05488
openalex publication_date 2017/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 k-decomposable 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 current author.