Year: 2016
Author: Bo Lu
Communications in Mathematical Research , Vol. 32 (2016), Iss. 4 : pp. 339–351
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.13447/j.1674-5647.2016.04.06
Communications in Mathematical Research , Vol. 32 (2016), Iss. 4 : pp. 339–351
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: $n$-injective module $n$-flat module $n$-Gorenstein injective module $n$-Gorenstein flat module preenvelope cover.