Koszul incidence algebras, affine semigroups, and Stanley-Reisner ideals

Victor Reiner, Dumitru Ioan Stamate

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

We prove a theorem unifying three results from combinatorial homological and commutative algebra, characterizing the Koszul property for incidence algebras of posets and affine semigroup rings, and characterizing linear resolutions of squarefree monomial ideals. The characterization in the graded setting is via the Cohen-Macaulay property of certain posets or simplicial complexes, and in the more general nongraded setting, via the sequential Cohen-Macaulay property.

Original languageEnglish (US)
Pages (from-to)2312-2345
Number of pages34
JournalAdvances in Mathematics
Volume224
Issue number6
DOIs
StatePublished - Aug 2010

Keywords

  • Affine semigroup
  • Incidence algebra
  • Koszul
  • Nongraded
  • Nonpure
  • Poset
  • Sequentially Cohen-Macaulay

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