Rees property and its related properties of ranked partially ordered sets

Abstract

Properties of ideals of a commutative Noetherian local ring or a Noetherian standerd graded commutative algebra over a field, called the Rees property, the second Rees property, the m-fullness and the fullness, can naturally be extended to the properties of ranked partially ordered sets. In this paper we study these properties with purely combinatorial points of view.