Abstract
Let be an injectively resolving subcategory of left -modules. We study a particular case of -Gorenstein injective and flat modules, called strongly -Gorenstein injective and flat modules, respectively. We prove that a module is -Gorenstein injective if and only if it is a direct summand of a strongly -Gorenstein injective module, and every -Gorenstein flat module is a direct summand of a strongly -Gorenstein flat module. Then we show the property of being a strongly -Gorenstein injective (resp. flat) module can be inherited by its direct summands under certain condition. The connections between (strongly) -Gorenstein injective and flat modules are also discussed. Finally, we investigate FC rings in terms of strongly -Gorenstein injective and flat modules.
Citation
Zenghui Gao. Ying Zhong. "STRONGLY -GORENSTEIN INJECTIVE AND FLAT MODULES." Rocky Mountain J. Math. 54 (1) 143 - 160, February 2024. https://doi.org/10.1216/rmj.2024.54.143
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