Cartan-Eilenberg X -内射和 X -平坦复形
Cartan-Eilenberg X -Injective and X -FlatComplexes
DOI: 10.12677/PM.2022.123039, PDF, HTML, 下载: 390  浏览: 561  国家自然科学基金支持
作者: 王亚丽：西北师范大学数学与统计学院，甘肃 兰州
关键词: CE X-内射复形；CE X-平坦复形；X-内射模；X-平坦模；CE X-Injective Complex； CE X-Flat Complex； X-Injective Module； X-Flat Module
摘要: 设 X 为一个左 R-模类。 本文引入了 CE X-内射复形和 CE X-平坦复形的概念，在 X 满足一定条件的情况下，讨论了这两类复形的联系，给出了这两类复形的一些等价刻画。
Abstract: Let X be a class of left R-modules. In this paper, the notions of CE X-injective complexes and CE X-flat complexes are introduced. Under certain mild assumptions on X , the relationship of CE X-injective complexes and CE X-flat complexes is discussed,and equivalent characterizations of CE X-injective complexes and CE X-flat complexes are given, respectively.
文章引用：王亚丽. Cartan-Eilenberg X -内射和 X -平坦复形[J]. 理论数学, 2022, 12(3): 354-367. https://doi.org/10.12677/PM.2022.123039

参考文献

[1] Cartan, H. and Eilenberg, S. (1957) Review. Homological Algebra, 41, 310-311.
https://doi.org/10.2307/3610160
[2] Verdier, J.L. (1996) Des cat´egories d´eriv´ees des cat´egories ab´eliennes. Ast´erisque, 239, 227-229.
[3] Enochs, E.E. (2011) Cartan-Eilenberg Complexes and Resolution. Journal of Algebra, 342,16-39.
https://doi.org/10.1016/j.jalgebra.2011.05.011
[4] Yang, G. and Liang, L. (2014) Cartan-Eilenberg Gorenstein Projective Complexes. Journal of Algebra and Its Applications, 13, Article ID: 1350068.
https://doi.org/10.1142/S0219498813500680
[5] Yang, G. and Liang, L. (2014) Cartan-Eilenberg Gorenstein Flat Complexes. Mathematica Scandinavica, 114, 5-25.
https://doi.org/10.7146/math.scand.a-16637
[6] Yang, G. and Liang, L. (2014) Stability of Cartan-Eilenberg Gorenstein Categories. Rendicontidel Seminario Matematico della Università di Padova, 132, 103-122.
https://doi.org/10.4171/RSMUP/132-8
[7] Stenstrom, B. (1970) Coherent Rings and FP-Injective Modules. Journal of the London Mathematical Society, 2, 323-329.
https://doi.org/10.1112/jlms/s2-2.2.323
[8] Gao, Z.H. and Wang, F.G. (2015) Weak Injective and Weak Flat Modules. Communications in Algebra, 43, 3857-3868.
https://doi.org/10.1080/00927872.2014.924128
[9] Zhu, Z.M. (2013) C-Coherent Rings, C-Semiherditary Rings and C-Regular Rings. Studia Scientiarum Mathematicarum Hungarica, 50, 491-508.
https://doi.org/10.1556/sscmath.50.2013.4.1256
[10] Lu, B. and Liu, Z.K. (2017) Cartan-Eilenberg FP-Injective Complexes. Journal of the Australian Mathematical Society, 103, 387-401.
https://doi.org/10.1017/S1446788716000586
[11] 马鹏举. Cartan-Eilenberg弱内射D弱平坦复形[D]: [硕士学位论文]. 兰州: 西北师范大学, 2018.
[12] Gobel, R. and Trlifaj, J. (2006) Approximations and Endomorphism Algebras of Modules. Walter de Gruyter, Berlin, New York.

为你推荐