In this work we give a characterization of Teter rings using the Macaulay inverse system. From this result we

recover the previou characterization obtained by Teter and Huneke-Vraciu.

This is a posdoctoral work with supervision of Joan Elias, Universitat de Barcelona, Catalunha.

Key-words: Macaulay inverse system, Gorenstein rings, Teter rings, Artin rings.