On \textit{w-FI}-flat and \textit{w-FI}-injective modules (Q2133619)

As we all know, flat modules and injective module are important in the study of homological algebra. In this vein, the authors introduce and study the concepts of \(w\)-FI-flat modules and \(w\)-FI-injective modules, which are in the context of the \(w\)-operation theory of FI-flat modules and FI-injective modules [\textit{L. Mao} and \textit{N. Ding}, J. Algebra 309, No. 1, 367--385 (2007; Zbl 1117.16002)]. The introduced modules are studied and compared with other classical modules. Among other things, they show that every module has a \(w\)-FI-flat cover. A couple of examples are also provided to illustrate the results.