On the Cohen-Macaulay property in commutative algebra and simplicial topology

Abstract

A ring R is called a "ring of sections" provided R is the section ring of a sheaf (A, X) of commutative rings defined over a base space X which is a finite partially ordered set given the order topology. Regard X as a finite abstract complex, where a chain in X corresponds to a simplex. In specific instances of (A, X), certain algebraic invariants of R are equivalent to certain topological invariants of X. © 1990 by Pacific Journal of Mathematics.