E-三角范畴中的(n, m)-强ξ-Gorenstein投射对象
(n, m)-Strongly ξ-Gorenstein Projective Objects in Extriangulated Categories
摘要: 设C是一个E-三角范畴，ξ是C中的一个E-三角真类。在C中引入(n, m)-强ξ-Gorenstein投射对象的概念，研究了C中的对象与其合冲的这种ξ-Gorenstein投射性质之间的联系。作为应用，证明了ξ中对象X的ξ-Gorenstein投射维数小于等于m当且仅当存在C中的ξ-Gorenstein投射对象G，使得是(1, m)-强ξ-Gorenstein投射的。
Abstract: Let C be an extriangulated category and ξ a proper class of E-triangles of C. The notion of (n, m)- strongly ξ-Gorenstein projective object in C is introduced and the relation of such ξ-Gorenstein projectivity of an object in C with that of its syzygies is investigated. As a consequence, it is shown that an object X of C has ξ-Gorenstein projective dimension at most m if and only if is (1, m)-strongly ξ-Gorenstein projective for some ξ-Gorenstein projective object of C.
文章引用：郭雯珺. E-三角范畴中的(n, m)-强ξ-Gorenstein投射对象[J]. 理论数学, 2024, 14(4): 268-275. https://doi.org/10.12677/pm.2024.144134

参考文献

[1] Nakaoka, H. and Palu, Y. (2019) Extriangulated Categories, Hovey Twin Cotorsion Pairs and Model Structures. Cahiers de Topologie et Géométrie Différentielle Catégoriques, 60, 117-193.
[2] Enochs, E.E. and Jenda, O.M.G. (1995) Gorenstein Injective and Projective Modules. Mathematische Zeitschrift, 220, 611-633. [Google Scholar] [CrossRef] 
[3] Auslander, M. and Brider, M. (1969) Stable Module Theory. Memoirs of the American Mathematical Society. American Mathematical Society, Providence. [Google Scholar] [CrossRef] 
[4] Enochs, E.E. and Jenda, O.M.G. (2000) Relative Homological Algebra. Walter de Gruyter Press, New York. [Google Scholar] [CrossRef] 
[5] Beligiannis, A. (2000) Relative Homological Algebra and Parity in Triangulated Categories. Journal of Algebra, 227, 268-361. [Google Scholar] [CrossRef] 
[6] Hu, J.S., Zhang, D.D. and Zhou, P.Y. (2020) Proper Classes and Gorensteinness in Extriangulated Categories. Journal of Algebra, 551, 23-60. [Google Scholar] [CrossRef] 
[7] He, Z.G. (2021) Gorenstein Objects in Extriangulated Categories. arXiv: 2011.14552.
[8] Hu, J.S., Zhang, D.D. and Zhou, P.Y. (2021) Gorenstein Homological Dimensions for Extriangulated Categories. Bulletin of the Malaysian Mathematical Sciences Society, 18, 2235-2252. [Google Scholar] [CrossRef] 
[9] Bennis, D. and Mahdou, N. (2007) Strongly Gorenstein Projective, Injective, and Lat Modules. Journal of Pure and Applied Algebra, 210, 437-445. [Google Scholar] [CrossRef] 
[10] Bennis, D. and Mahdou, N. (2009) A Generalization Strongly Gorenstein Projective Modules. Journal of Algebra and Its Applications, 8, 219-227. [Google Scholar] [CrossRef] 
[11] Bennis, D. (2009) (n; m)-Strongly Gorenstein Projective Modules. International Electronic Journal of Algebra, 6, 119-133.
[12] 常雯雯, 高楠. 三角范畴中的(n, m)-强ξ-Gorenstein投射对象[J]. 应用数学与计算数学学报, 2014, 28(2): 166-174.
[13] Rotman, J.J. (1979) An Introduction to Homological Algebra. Academic Press, New York.

为你推荐