A STRUCTURAL INVARIANT ON CERTAIN TWO-DIMENSIONAL NOETHERIAN PARTIALLY ORDERED SETS

If (X,≤X) is a partially ordered set satisfying certain necessary conditions for X to be order-isomorphic to the spectrum of a Noetherian domain of dimension two, we describe a new poset (StrX,≤StrX) that completely determines X up to isomorphism. The order relation ≤StrX imposed on StrX is modeled after R. Wiegand’s well-known “P5” condition that can be used to determine when a given partially ordered set (U,≤U ) of a certain type is order-isomorphic to (SpecZ[x],⊆).