TY - JOUR
T1 - A Generalization of Gorenstein Injective and Flat Modules
AU - Lu , Bo
JO - Communications in Mathematical Research 
VL - 4
SP - 339
EP - 351
PY - 2021
DA - 2021/05
SN - 32
DO - http://doi.org/10.13447/j.1674-5647.2016.04.06
UR - https://global-sci.org/intro/article_detail/cmr/18906.html
KW - $n$-injective module, $n$-flat module, $n$-Gorenstein injective module, $n$-Gorenstein flat module, preenvelope, cover.
AB - <p style="text-align: justify;">In this article, we introduce and study the concept of $n$-Gorenstein injective (resp., $n$-Gorenstein flat) modules as a nontrivial generalization of Gorenstein
injective (resp., Gorenstein flat) modules. We investigate the properties of these modules in various ways. For example, we show that the class of $n$-Gorenstein injective
(resp., $n$-Gorenstein flat) modules is closed under direct sums and direct products for $n ≥ 2$. To this end, we first introduce and study the notions of $n$-injective modules
and $n$-flat modules.</p>