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arXiv · 2412.01392

Quasilifting of hulls and depth of tensor product of modules

Sutapa Dey·Amit Tripathi
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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 $\mathcal{TE}$ rings. Some general conditions on the existence of hulls and approximations are also studied.

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Sutapa Dey, Amit Tripathi. 2024-12-02. Quasilifting of hulls and depth of tensor product of modules. https://arxiv.org/abs/2412.01392

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