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Volume 32, Issue 4
A Generalization of Gorenstein Injective and Flat Modules

Bo Lu

DOI: 10.13447/j.1674-5647.2016.04.06

Commun. Math. Res., 32 (2016), pp. 339-351.

Published online: 2021-05

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  • 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.

  • Keywords

$n$-injective module, $n$-flat module, $n$-Gorenstein injective module, $n$-Gorenstein flat module, preenvelope, cover.

  • AMS Subject Headings

16D40, 13E15, 16D50, 18G25

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-32-339, author = {Lu , Bo}, title = {A Generalization of Gorenstein Injective and Flat Modules}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {32}, number = {4}, pages = {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.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2016.04.06}, url = {http://global-sci.org/intro/article_detail/cmr/18906.html} }
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 -

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.

Bo Lu. (2021). A Generalization of Gorenstein Injective and Flat Modules. Communications in Mathematical Research . 32 (4). 339-351. doi:10.13447/j.1674-5647.2016.04.06
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