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Koszul Algebras and Computations

  • Anna M. BigattiEmail author
  • Emanuela De Negri
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2176)

Abstract

A Koszul algebra R is a \(\mathbb{N}\)-graded K-algebra whose residue field K has a linear free resolution as an R-module. Many papers and lectures have been given on this topic, so here we collect various properties and facts which are related to being a Koszul algebra, and illustrate their mutual implications or counter-examples.

In addition we explain how one can investigate computationally these many aspects, some of which would seem to be intrinsically intractable, and we show many examples by using CoCoA-5.

Keywords

Complete Intersection Polynomial Ring Betti Number Hilbert Series Homogeneous Ideal 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità degli Studi di GenovaGenovaItaly

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