FP-injective dimensions and Gorenstein homology

IF 0.7 3区数学 Q2 MATHEMATICS

Proceedings of the Edinburgh Mathematical Society Pub Date : 2022-11-01 DOI:10.1017/S0013091522000542

Gang Yang, Junpeng Wang

引用次数: 0

Abstract

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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fp -内射维数与Gorenstein同调

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Proceedings of the Edinburgh Mathematical Society 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： The Edinburgh Mathematical Society was founded in 1883 and over the years, has evolved into the principal society for the promotion of mathematics research in Scotland. The Society has published its Proceedings since 1884. This journal contains research papers on topics in a broad range of pure and applied mathematics, together with a number of topical book reviews.