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arXiv · 2609.37967

Weak and Serre Lifting of Cyclic Modules and the Liftability of Auslander Duals

Shashi Ranjan Sinha·Amit Tripathi
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Abstract

Let $Q$ be a local ring and $f$ a nonzerodivisor on $Q.$ We investigate the weak and Serre lifting properties of cyclic modules over $R = Q/(f)$ to $Q.$ First, we establish characterization for the weak and Serre liftability of these modules and provide sufficient conditions under which their tensor products share these properties. We present an example that strengthens a counterexample of Nawaz and Levins and answers a question of Jorgensen. Finally, we also study the liftability of Auslander duals, obtaining a mild strengthening of a theorem of Ghosh and Samanta.

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Shashi Ranjan Sinha, Amit Tripathi. 2026-09-29. Weak and Serre Lifting of Cyclic Modules and the Liftability of Auslander Duals. https://arxiv.org/abs/2609.37967

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