FPn-Injective, FPn-Flat Covers and Preenvelopes, and Gorenstein AC-Flat Covers  

作　　者：Daniel Bravo Sergio Estrada Alina Iacob 

机构地区：[1]Instituto de Ciencias Fisicas y Matematicas, Facultad de Ciencias Universidad Austral de Chile, Valdivia, Chile [2]Departamento de Matematicas, Universidad de Murcia Campus de Espinardo, 30100 Murcia, Spain [3]Department of Mathematical Sciences, Georgia Southern University Statesboro, GA 30460, U.S.A

出　　处：《Algebra Colloquium》2018年第2期319-334,共16页代数集刊（英文版）

摘　　要：We prove that, for any n 〉 2, the classes of FPn-injective modules and of FPn-flat modules are both covering and preenveloping over any ring R. This includes the case of FP∞-injective and FP∞-flat modules （i.e., absolutely clean and, respectively, level modules）. Then we consider a generalization of the class of （strongly） Gorenstein flat modules, i.e., the （strongly） Gorenstein AC-flat modules （cycles of exact complexes of flat modules that remain exact when tensored with any absolutely clean module）. We prove that some of the properties of Gorenstein fiat modules extend to the class of Gorenstein AC-flat modules; for example, we show that this class is precovering over any ring R. We also show that （as in the case of Gorenstein flat modules） every Gorenstein AC-flat module is a direct summand of a strongly Gorenstein AC-flat module. When R is such that the class of Gorenstein AC-flat modules is closed under extensions, the converse is also true. Moreover, we prove that if the class of Gorenstein AC-flat modules is closed under extensions, then it is covering.

关 键 词：FPn-injective module FPn-flat module Ding injective module GorensteinAC-flat module 

分 类 号：TP212[自动化与计算机技术—检测技术与自动化装置] TU241.2[自动化与计算机技术—控制科学与工程]