On the Koszul property of toric face rings

  title={On the Koszul property of toric face rings},
  author={Dang Hop Nguyen},
Toric face rings is a generalization of the concepts of affine monoid rings and Stanley-Reisner rings. We consider several properties which imply Koszulness for toric face rings over a field $k$. Generalizing works of Laudal, Sletsj\o{}e and Herzog et al., graded Betti numbers of $k$ over the toric face rings are computed, and a characterization of Koszul toric face rings is provided. We investigate a conjecture suggested by R\"{o}mer about the sufficient condition for the Koszul property. The… CONTINUE READING