Collectanea Mathematica

, Volume 69, Issue 3, pp 451–477 | Cite as

The structure of the inverse system of level K-algebras

  • Shreedevi K. Masuti
  • Laura TozzoEmail author


Macaulay’s inverse system is an effective method to construct Artinian K-algebras with the additional properties of being, for example, Gorenstein, level, or having any specific socle type. Recently, Elias and Rossi (Adv Math 314:306–327, 2017) gave the structure of the inverse system of d-dimensional Gorenstein K-algebras for any \(d>0\). In this paper we extend their result by establishing a one-to-one correspondence between d-dimensional level K-algebras and suitable submodules of the divided power ring. We give several examples to illustrate our result.


Macaulay’s inverse system Level K-algebras Divided power ring Gorenstein K-algebras 

Mathematics Subject Classification

13A02 13H10 13J05 13F20 



The first author was supported by INdAM COFOUND Fellowships cofounded by Marie Curie actions, Italy. We thank our advisor M. E. Rossi for suggesting the problem and providing many useful ideas throughout the preparation of this manuscript. We thank Juan Elias for providing us the updated version of Inverse-syst.lib and clarifying our doubts in Singular. We would also like to thank Alessandro De Stefani for providing us the proof of Proposition 4(b) in the one-dimensional case, and Aldo Conca and Matteo Varbaro for useful discussions on the examples of level rings.


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Copyright information

© Universitat de Barcelona 2018

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di GenovaGenoaItaly
  2. 2.Department of MathematicsUniversity of KaiserslauternKaiserslauternGermany

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