Combinatorial properties of ``cleanness''
type: Item
instance of: scholarly article
title: Combinatorial properties of ``cleanness''
zbMATH Open document ID: 0855.13013
author: Robert Samuel Simon
published in: Journal of Algebra
publication date: 1994-08-16T00:00:00Z
review text: \textit{N. Bourbaki} defines a composition series of a finitely generated module \(M\) over a commutative Noetherian ring \(R\) to be a finite sequence \(O = M_0 \subset M_1\) \(\subset \dots \subset M_n = M\) of submodules of \(M\) with \(M_i/M_{i - 1} \cong R/P_i\) for a prime ideal \(P_i\) of \(R\), for \(1 \leq i \leq n\). The author calls \(M\) clean if it has a composition series for which each prime \(P_i\) occurring is minimal over the annihilator of \(M\) in \(R\). This paper is a study of this concept, its basic properties and its connections with the shelling of simplicial complexes.
Mathematics Subject Classification ID: 13E15
Mathematics Subject Classification ID: 13E05
Mathematics Subject Classification ID: 55N10
zbMATH DE Number: 614214
zbMATH Keywords: clean module
zbMATH Keywords: composition series of a finitely generated module
zbMATH Keywords: simplicial complexes
reviewed by: Kenneth A. Brown
MaRDI profile type: Publication
full work available at URL: jabr.1994.1191
OpenAlex ID: W2026935521
DOI: 10.1006/JABR.1994.1191
description: scientific article; zbMATH DE number 614214