Combinatorial Properties of "Cleanness" Original Research Article

"Cleanness" is defined as the existence of a "composition series" (Bourbaki′s definition) of a Noetherian module such that the annihilators of the factor modules are the minimal prime ideals associated to the module. As applied to the factor rings of monomial ideals, the combinatorial properties of cleanness are explored, especially as they relate to the shellability of simplicial complexes. With the aid of the cleanness concept, the definition of matroids is extended to multiset systems and shelling extensions are explored.