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Weak Gorenstein Graded Modules

Yanhui SONG(), Ting GUO
School of General Education, Lanzhou University of Information Science and Technology, Lanzhou Gansu 730300, China
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Abstract

Let R be a graded ring. The concepts of weak Gorenstein gr-projective modules, gr-injective modules and gr-flat modules are introduced, and some homological characterizations of weak Gorenstein gr-projective modules are given. It is shown that a weak Gorenstein gr-projective module is a Gorenstein gr-projective R-module over a graded n-Gorenstein ring R. Moreover, it is proved that: if any graded injective R-module has a finite graded flat dimension, then a graded module M is weak Gorenstein gr-flat if and only if M is Gorenstein gr-flat.

Keywords

gr-projective moduleweak Gorenstein gr-projective modulegraded flat dimensionweak Gorenstein gr-flat module
Article ID: 2096-7675(2024)05-0556-06

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Journal of Xinjiang University(Natural Science Edition in Chinese and English)
Volume 41 Issue 5,
September 2024
Pages 556-561
DOI: 10.13568/j.cnki.651094.651316.2024.01.30.0001
Cite this article:
SONG Y, GUO T. Weak Gorenstein Graded Modules. Journal of Xinjiang University(Natural Science Edition in Chinese and English), 2024, 41(5): 556-561. https://doi.org/10.13568/j.cnki.651094.651316.2024.01.30.0001
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