Inverse Systems of Local Rings

  • Juan EliasEmail author
Part of the Lecture Notes in Mathematics book series (LNM, volume 2210)


Matlis duality and the particular case of Macaulay correspondence provide a dictionary between the Artin algebras and their inverse systems. Inspired in a result of Emsalem we translate the problem of classification of Artin algebras to a problem of linear system of equations on the inverse systems.

The main purpose of these notes is to use this result to classify Artin Gorenstein algebras with Hilbert function {1, 3, 3, 1}, level algebras and compressed algebras. The main results presented in these notes were obtained in collaboration with M.E. Rossi.



I am grateful to Le Tuan Hoa and to Ngo Viet Trung for giving me the opportunity to speak about one of my favorite subjects. I am also grateful to the participants for their kind hospitality and mathematical discussions that made a very interesting and productive month in the city of Hanoi. We thank to Marcela Silva and Roser Homs for their useful comments and remarks. Last but not least, I am greatly indebted to M. E. Rossi for a long time collaboration on Macaulay’s inverse systems and other topics. Some of the main results of these notes are made in collaboration with M. E. Rossi.


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department de Matemàtiques i InformàticaUniversitat de BarcelonaBarcelonaSpain

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