On algebras associated to partially ordered sets

Abstract

We continue the study on sheaves of rings on finite posets. We present examples where the ring of global sections coincide with toric faces rings, quotients of a polynomial ring by a monomial ideal and algebras with straightening laws. We prove a rank-selection theorem which generalizes the well-known rank-selection theorem of Stanley-Reisner rings. Finally, we determine an explicit presentation of certain global rings of sections.

14 pages

References in corpus (3)

• Combinatorial characterizations of generalized Cohen-Macaulay monomial ideals
• Cohomology of partially ordered sets and local cohomology of section rings
• h-vectors of Gorenstein* simplicial posets

Cited by in corpus (7)

• On toric face rings
• Cohomology of partially ordered sets and local cohomology of section rings
• Seminormality and local cohomology of toric face rings
• On some local cohomology spectral sequences
• Polyhedral products over finite posets
• Stanley-Reisner rings for symmetric simplicial complexes, G-semimatroids and Abelian arrangements
• On canonical modules of toric face rings