On the Regularity and Koszulness of Modules Over Local Rings

Abstract

Koszul modules over Noetherian local rings R were introduced by Herzog and Iyengar and they possess good homological properties, for instance their Poincaré series is rational. It is an interesting problem to characterize classes of Koszul modules. Following the idea traced by Avramov, Iyengar, and Sega, we take advantage of the existence of special filtration on R for proving that large classes of R-modules over Koszul rings are Koszul modules. By using this tool we reprove and extend some results obtained by Fitzgerald.

Key Words:

• Koszul algebra
• Koszul module
• Linear resolution
• Poincaré series
• Regularity

2010 Mathematics Subject Classification:

• 13D02
• 13D07
• 16W50
• 16S37

ACKNOWLEDGMENTS

This work was done while the author visiting University of Genoa, Italy. He is thankful to the university for the hospitality. He would like to give special thanks to Professor Maria Evelina Rossi for her guidance and valuable comments. The author also wish to thank A. Conca, M. Jahangiri, and M. Mandal for many stimulating discussions.

The author also would like to thank the referee for his/her valuable comments.

Notes

Communicated by I. Swanson.