强n-Gorenstein FC-投射模
Strongly n-Gorenstein FC-Projective Modules
摘要: 引入了强n-Gorenstein FC-投射模，给出了强n-Gorenstein FC-投射模的一些性质，证明了对任意模M和非负整数n，R-模M的Gorenstein FC-投射维数不超过n当且仅当M是强n-Gorenstein FC-投射模的直和因子时。
Abstract: In this paper, strongly n-Gorenstein FC-projective modules are introduced, some properties of them are presented. For arbitrary module M and nonnegative integral number n, the Gorenstein FC-projective dimensions of M are not larger than n if and only if M is direct summand of a strongly n-Gorenstein FC-Projective module.
文章引用：杨富霞, 张翠萍. 强n-Gorenstein FC-投射模[J]. 理论数学, 2020, 10(10): 974-979. https://doi.org/10.12677/PM.2020.1010114

参考文献

[1] Auslander, M. and Bridger, M. (1969) Stable Module Theory. In: Memoirs of the American Mathematical Societyc, Amer. Math. Soc, Providence, RI, Vol. 94. [Google Scholar] [CrossRef] 
[2] Enochs, E.E. and Jenda, O.M.G. (1995) Gorenstein Injective and Projective Modules. Mathematische Zeitschrift, 220, 611-633. [Google Scholar] [CrossRef] 
[3] Holm, H. (2004) Gorenstein Homological Dimensions. Journal of Pure and Applied Algebra, 189, 167-193. [Google Scholar] [CrossRef] 
[4] Mahdou, N. and Tamekkante, M. (2009) Strongly n-Gorenstein Projective, Injective and Flat Modules. Proceedings of the American Mathematical Society, 143, 235-251.
[5] 刘仲奎, 刘妍平. 强n-Gorenstein C-投射模和内射模[J]. 西北师范大学学报(自然科学版), 2013, 49(4): 1.
[6] Gao, Z. and Jenda, H. (2013) On Strongly Gorenstein FP-Injective Modules. Communications in Algebra, 25, 3035-3044. [Google Scholar] [CrossRef] 
[7] Wang, Y. and Zhou, D.X. (2020) Gorenstein FC-Projective Modules. Journal of Algebra and Its Applications, 19, Article ID 2050066. [Google Scholar] [CrossRef] 
[8] Xue, W.M. (1999) On N-Presented Modulesand Almost Ex-cellent Extensions. Communications in Algebra, 27, 1091-1102. [Google Scholar] [CrossRef] 
[9] 王玉, 周德旭. 关于强Gorenstein FC-投射模[J]. 福建师范大学学报(自然科学版), 2018, 34(5): 18-24.
[10] Huang, Z.Y. (2013) Proper Resolutions and Gorenstein Categories. Journal of Algebra, 393, 142-169. [Google Scholar] [CrossRef] 
[11] Enochs, E.E. and Jenda, O.M.G. (2000) Relative Homological Algebra. In: de Gruyter Expositions Mathematics, Vol. 30, Walter de Gruyter, Berlin.

为你推荐