Cohen-Macaulay rings of sections (Q1088735)

This paper introduces and investigates the class of rings of sections of flasque sheaves of regular commutative algebras on finite posets. The main result gives a necessary and sufficient condition for these rings to be Cohen-Macaulay in terms of certain topological properties of the poset. It is a generalization and a new proof of Reisner's theorem whih characterizes Cohen-Macaulay quotients of polynomial rings by ideals generated by squarefree monomials [\textit{G. A. Reisner}, Adv. Math. 21, 30-49 (1976; Zbl 0345.13017)]. The author also illustrates by examples other possible applications of his main result.