CLC number: O154.2

A Note on Projectively Coresolved Gorenstein Flat Complexes and Dimensions

关于PGF复形和维数的注记

¹ College of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, Gansu, China
² Gansu Provincial Research Center for Basic Disciplines of Mathematics and Statistics, Lanzhou 730070, Gansu, China

^† Corresponding author. E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 10 April 2025

Abstract

In this article, we first establish a recollement related to projectively coresolved Gorenstein flat (PGF) complexes. Secondly, we define and study PGF dimension of complexes, we denote it PGF(X) for a complex X. It is shown that the PGF(X) is equal to the infimum of the set {supA | there exists a diagram of morphisms of complexes A←G→X, such that G→X is a special PGF precover of X and G→A is a PGF almost isomorphism}.

摘要

首先，建立了相对于projectively coresolved Gorenstein flat (PGF)复形的粘合。其次，定义并研究了PGF维数，对于任意的复形X，将其PGF维数记作PGF(X)。得到了PGF(X)是$\{\mathrm{s}\mathrm{u}\mathrm{p}A|\mathrm{存在}\mathrm{复形}\mathrm{的态}\mathrm{射图}A\leftarrow G\to X,\mathrm{使}$$\mathrm{得}G\to X\mathrm{是}X\mathrm{的特}\mathrm{殊}\mathrm{P}\mathrm{G}\mathrm{F}\mathrm{预覆}\mathrm{盖}$，$\mathrm{且}G\to A\mathrm{是}\mathrm{P}\mathrm{G}\mathrm{F}\mathrm{几乎}\mathrm{同构}\}$的下确界。