LI Wei,GAO Zenghui.A Characterization of n-Strongly Gorenstein FP-gr-injective Modules[J].Journal of Chengdu University of Information Technology,2025,40(05):704-709.[doi:10.16836/j.cnki.jcuit.2025.05.019]
n-强Gorenstein FP-gr-内射模的刻画
- Title:
- A Characterization of n-Strongly Gorenstein FP-gr-injective Modules
- 文章编号:
- 2096-1618(2025)05-0704-06
- Keywords:
- FP-gr-injective module; n-strongly Gorenstein FP-gr-injective module; n-strongly Gorenstein gr-flat module; gr-coheren tring
- 分类号:
- O154.2
- 文献标志码:
- A
- 摘要:
- 设R是分次环且n是一个正整数。引入并研究n-强Gorenstein FP-gr-内射模。对于正整数n>m,举例说明n-强Gorenstein FP-gr-内射模未必是m-强Gorenstein FP-gr-内射模,并刻画n-强Gorenstein FP-gr-内射模的诸多性质。在gr-凝聚环上讨论n-强Gorenstein FP-gr-内射模与n-强Gorenstein gr-平坦模的关系,以及n-强Gorenstein FP-内射模在分次与未分次情形下的联系。
- Abstract:
- Let R be a graded ring and n a positive integer.In this paper,we introduce and study n-strongly GorensteinFP-gr-injective module.An example is given to show that n-strongly Gorenstein FP-gr-injective modules need not be m-strongly Gorenstein FP-gr-injective modules whenever n>m,and many properties of n-strongly Gorenstein FP-gr-injective modules arecharacterized.Then the relationships between n-strongly Gorenstein FP-gr-injective modules and n-strongly Gorenstein gr-flat modules over gr-coherent rings are discussed.Finally,the connections between the graded and the ungraded n-strongly Gorenstein FP-injective modules are considered.
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备注/Memo
收稿日期:2024-05-16
基金项目:国家自然科学基金资助项目(12371038); 四川省自然科学基金面上资助项目(2024NSFSC0417)
通信作者:高增辉.E-mail:gaozenghui@cuit.edu.cn