Testing for the Gorenstein property

• Autores: Olgur Celikbas, Sean Sather-Wagstaff
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 67, Fasc. 3, 2016, págs. 555-568
• Idioma: inglés
• DOI: 10.1007/s13348-015-0163-x
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• Resumen

  • We answer a question of Celikbas, Dao, and Takahashi by establishing the following characterization of Gorenstein rings: a commutative noetherian local ring (R,\mathfrak m) is Gorenstein if and only if it admits an integrally closed \mathfrak m-primary ideal of finite Gorenstein dimension. This is accomplished through a detailed study of certain test complexes. Along the way we construct such a test complex that detect finiteness of Gorenstein dimension, but not that of projective dimension.