2017/05/18 by Gheibi, Mohsen, Takahashi, Ryo
#13C13 #13D40 #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.1705.06563
We study Cohen-Macaulay non-Gorenstein local rings (R,\mathfrakm,k) admitting certain totally reflexive modules. More precisely, we give a description of the Poincaré series of k by using the Poincaré series of a non-zero totally reflexive module with minimal multiplicity. Our results generalize a result of Yoshino to higher-dimensional Cohen-Macaulay local rings. Moreover, from a quasi-Gorenstein ideal satisfying some conditions, we construct a family of non-isomorphic indecomposable totally reflexive modules having an arbitrarily large minimal number of generators.