循环模的弱提升与Serre提升及Auslander对偶的可提升性
Weak and Serre Lifting of Cyclic Modules and the Liftability of Auslander Transposes
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中文总结 AI 辅助
本文研究局部环商环上循环模的弱提升与Serre提升性质，给出刻画及张量积保持条件，并加强相关反例与定理，同时探讨Auslander对偶的可提升性。
中文摘要 AI 辅助
设 $Q$ 为局部环，$f$ 为 $Q$ 上的非零因子。我们研究 $R = Q/(f)$ 上循环模到 $Q$ 的弱提升与Serre提升性质。首先，我们建立了这些模的弱可提升性与Serre可提升性的刻画，并给出了其张量积共享这些性质的充分条件。我们给出一个例子，加强了Nawaz和Levins的反例，并回答了Jorgensen的一个问题。最后，我们还研究了Auslander对偶的可提升性，得到了Ghosh和Samanta定理的一个适度加强。
英文摘要
Let $Q$ be a local ring, $f$ a nonzerodivisor, and $R=Q/(f)$. We characterize weak and Serre liftability of cyclic $R$-modules under suitable hypotheses, obtaining complete-intersection criteria for Serre liftability in small height. We prove that the tensor product of two weakly liftable cyclic modules remains weakly liftable when their first Tor module vanishes, and give sufficient conditions for tensor products to preserve Serre liftability. We construct an Artinian Gorenstein quotient $Q/I$, with $Q$ regular, that is perfect over $R$ and Serre liftable but not weakly liftable to $Q$, showing that the negative answer to a question of Jorgensen persists in this more restrictive setting. Finally, we characterize when a lift induces a lift of the Auslander transpose and obtain a freeness criterion related to the Auslander-Reiten conjecture, recovering a theorem of Ghosh and Samanta.
发表机构
- Indian Institute of Technology – Hyderabad（印度理工学院海德拉巴分校）
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