2015/04/29 by Celikbas, Olgur, Sather-Wagstaff, Sean
#13B22 #13D02 #13D07 #13D09 #13H10 #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.1504.08014
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.