J\"urgen Herzog and Srikanth Iyengar

Koszul modules

Abstract.
This paper introduces a new class of modules over noetherian local rings,
called Koszul modules. It is proved that when a local ring $R$ is either
a complete intersection or Golod, all high syzygies of finitely generated
$R$-modules are Koszul. A stronger result is obtained when $R$ is Golod:
the ($2$\,emb\,dim $R + 1$)st syzygy of every $R$-module is Koszul. In
addition, results are established that demonstrate that Koszul modules
possess good homological properties; for instance, their Poincar\'e series
is a rational function.