fp -内射维数与Gorenstein同调

Pub Date : 2022-11-01 DOI:10.1017/S0013091522000542

Gang Yang, Junpeng Wang

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引用次数: 0

摘要

设$R$是左相干环。证明了如果$R$-模$M$具有有限的FP-内射维数，则Gorenstein投影（分别为Gorenstein-flat）维数和投影（分别是flat）维度重合。此外，我们还得到了在一些温和条件下，该对（$\mathcal｛GP｝，\，\mathcal{GP｝^｛\perp｝$）形成了一个投影余项对。

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FP-injective dimensions and Gorenstein homology

Abstract Let $R$ be a left coherent ring. It is proven that if an $R$-module $M$ has a finite FP-injective dimension, then the Gorenstein projective (resp. Gorenstein flat) dimension and the projective (resp. flat) dimension coincide. Also, we obtain that the pair ($\mathcal {GP},\, \mathcal {GP}^{\perp }$) forms a projective cotorsion pair under some mild conditions.

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