极大余挠模
Max-Cotorsion Modules
DOI: 10.12677/PM.2023.135138, PDF, HTML, 下载: 210  浏览: 255 
作者: 杨娟妮*, 杨晓燕：西北师范大学，数学与统计学院，甘肃 兰州
关键词: 极大余挠模；极大平坦模；余挠对br>Max-Cotorsion Module； Max-Flat Module； Cotorsion Pair
摘要: 本文研究了极大余挠模的一些判定和同调性质，证明了极大平坦模类与极大余挠模类构成了完全且遗传的余挠对。
Abstract: In this paper, we study some criterions and homological properties of max-cotorsion modules. It is proved that the class of max-flat modules and the class of max-cotorsion modules is a perfect and hereditary cotorsion pair.
文章引用：杨娟妮, 杨晓燕. 极大余挠模[J]. 理论数学, 2023, 13(5): 1355-1362. https://doi.org/10.12677/PM.2023.135138

参考文献

[1] Harrison, D.K. (1959) Infinite Abelian Groups and Homological Methods. Annals of Mathe- matics, 69, 336-391.
https://doi.org/10.2307/1970188
[2] Xu J. (1996) Flat Covers of Modules. In: Lecture Notes in Mathematics, Vol. 1634, Springer- Verlag, Berlin.
[3] Trlifaj, J. (2000) Covers, Envelopes and Cotorsion Theories. Lecture Notes for the Workshop "Homological Methods in Module Theory", Cortona, 10-16 September 2000.
[4] Mao, L.X. and Ding, N.Q. (2005) Notes on Cotorsion Modules. Communications in Algebra, 33, 349-360.
https://doi.org/10.1081/AGB-200041029
[5] Xiang, Y. (2010) Max-Injective, Max-Flat Modules and Max-Coherent Ring. Bulletin of the Korean Mathematical Society, 47, 611-622.
https://doi.org/10.4134/BKMS.2010.47.3.611
[6] Alagoz, Y. and Buyukasik, E. (2021) On Max-Fat Modules and Max-Cotorsion Modules. Ap- plicable Algebra in Engineering, 32, 195-215.
https://doi.org/10.1007/s00200-020-00482-4
[7] Enochs, E.E. and Jenda, O.M.G. (2000) Relative Homological Algebra. Walter de Gruyter, New York.
https://doi.org/10.1515/9783110803662
[8] Enochs, E.E. (2002) Covers, Envelopes and Cotorsion Theories. Nova Biomedical, New York.
[9] 于梅菊, 方咏梅. 探研极大平坦维数[J]. 通化师范学院学报, 2010, 31(12): 11-13.
[10] Rotman, J.J. (2009) An Introduction to Homological Algebra. Springer, New York.
https://doi.org/10.1007/b98977
[11] Holm, H. and Jorgensen, P. (2008) Covers, Precovers, and Purity. Illinois Journal of Mathe- matics, 52, 691-703.
https://doi.org/10.1215/ijm/1248355359

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