Quasilifting of hulls and depth of tensor product of modules

2024/12/02 by Dey, Sutapa, Tripathi, Amit
#13C15 (Secondary) #13D07 (Primary) 13C14 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2412.01392

Abstract

We investigate the depth of the tensor product of finitely generated modules over local rings. One of the main ingredients of our approach is a lifting construction introduced by Huneke, Jorgensen, and Wiegand. We recover a result of Celikbas, Sadeghi, and Takahashi for local complete intersection rings. Additionally, we provide a negative answer to a question they asked and establish a corresponding lower bound. We derive a result on the depth of the tensor product of certain modules over local complete TE rings. Some general conditions on the existence of hulls and approximations are also studied.

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