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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 completeT Erings. Some general conditions on the existence of hulls and approximations are also studied.

Quasilifting of hulls and depth of tensor product of modules