拟-Gorenstein 平坦模与维数
Quasi-Gorenstein Flat Modules andDimensions
摘要: 本文主要研究了拟-Gorenstein平坦模及其基本性质,并探讨了其相对于短正合列的有关结论。同时,描述了有限拟-Gorenstein平坦同调维数。
Abstract: In this paper, we investigate quasi-Gorenstein flat modules and their basic properties, and study the relative conclusions of this module class respect to short exact sequence. Simultaneously, we describe finite quasi-Gorenstein flat homological dimensions.
文章引用:辛红娟. 拟-Gorenstein 平坦模与维数[J]. 理论数学, 2023, 13(5): 1440-1446. https://doi.org/10.12677/PM.2023.135148

参考文献

[1] Auslander, M. and Bridger, M. (1969) Stable Module Theory. Memoirs of the American Math- ematical Society, 94.
https://doi.org/10.1090/memo/0094
[2] Enochs, E.E. and Jenda, O. (1995) Gorenstein Injective and Projective Modules. Mathematis- che Zeitschrift, 220, 611-633.
https://doi.org/10.1007/BF02572634
[3] Enochs, E.E., Jenda, O. and Torrecillas, B. (1993) Gorenstein Flat Modules. Journal of Nanjing University (Natural Sciences), 10, 1-9.
[4] Mashhad, F.M.A. (2022) Quasi-Gorenstein Projective and Quasi-Gorenstein Injective Modules. International Journal of Mathematics, 33, Article 2250086.
https://doi.org/10.1142/S0129167X22500860
[5] Fuchs, L. (1969) On Quasi-Injective Modules. The Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 23, 541-546.
[6] Enochs, E.E. and Jenda, O. (2000) Relative Homological Algebra. In: De Gruyter Expositions in Mathematics, Vol. 30, Walter de Gruyter, Berlin, New York.
[7] Henrik, H. (2004) Gorenstein Homological Dimensions. Journal of Pure and Applied Algebra, 189, 167-193.
https://doi.org/10.1016/j.jpaa.2003.11.007