标题： 拟提升的包络和模的张量积的深度 显示英文标题

标题： Quasilifting of hulls and depth of tensor product of modules

摘要： 我们研究局部环上有限生成模的张量积的深度。 我们方法的主要成分之一是Huneke、Jorgensen和Wiegand引入的提升构造。 我们恢复了Celikbas、Sadeghi和Takahashi对于局部完满交环的结果。 此外，我们提供了对他们提出的问题的否定回答，并建立了相应的下界。 我们推导了局部完满$\mathcal{TE}$ 环上某些模的张量积的深度结果。 还研究了一些关于hulls和近似存在性的普遍条件。 显示英文摘要

摘要： 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 $\mathcal{TE}$ rings. Some general conditions on the existence of hulls and approximations are also studied.