Combinatorial properties of ``cleanness''
\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.
composition series of a finitely generated module
scientific article; zbMATH DE number 614214