On the Regularity and Koszulness of Modules Over Local Rings |
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Authors: | Rasoul Ahangari Maleki |
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Affiliation: | 1. School of Mathematics , Institute for Research in Fundamental Sciences (IPM) , Tehran , Iranand Faculty of Mathematical Sciences and Computer Kharazmi University, Tehran, Iranrasoulahangari@gmail.com;4. std_ahangari@khu.ac.ir |
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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. |
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Keywords: | Koszul algebra Koszul module Linear resolution Poincaré series Regularity |
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