态射和短正合列的预包络关于直和的封闭性
Preenvelope of Morphisms and Short Exact Sequences on the Closure ofDirect Sum
DOI: 10.12677/PM.2023.135153, PDF, HTML, 下载: 190  浏览: 240 
作者: 刘诗瑶*, 杨晓燕:西北师范大学,数学与统计学院,甘肃 兰州
关键词: 预包络直和封闭性Preenvelope Direct Sum Closure
摘要: 本文利用左 R-模的预包络关于直和的封闭性, 研究了态射和短正合序列的预包络关于直和的封闭性。
Abstract: In this paper, we study that the preenvelopes of morphisms and short exact sequences are closed under direct sums using the fact that the preenvelope of left R-module is closed under direct sums.
文章引用:刘诗瑶, 杨晓燕. 态射和短正合列的预包络关于直和的封闭性[J]. 理论数学, 2023, 13(5): 1508-1515. https://doi.org/10.12677/PM.2023.135153

参考文献

[1] Enochs, E.E. (1981) Injective and Flat Covers, Envelopes and Resolents. Israel Journal of Mathematics, 39, 189-209.
https://doi.org/10.1007/BF02760849
[2] Auslander, M. and Smal∅, S. (1980) Preprojective Modules over Artin Algebras. Journal of Algebra, 66, 61-122.
https://doi.org/10.1016/0021-8693(80)90113-1
[3] Fu, X.H., Guil Asensio, P.A., Herzog, I. and Torrecillas, B. (2013) Ideal Approximation Theory. Advances in Mathematics, 244, 750-790.
https://doi.org/10.1016/j.aim.2013.05.020
[4] Mao, L.X. (2018) On Preenvelopes and Precovers by Ideals of Morphisms of Modules. Journal of Pure and Applied Algebra, 222, 4004-4019.
https://doi.org/10.1016/j.jpaa.2018.02.017
[5] Mao, L.X. (2020) On Envelopes and Covers in the Category of Short Exact Sequences. Bulletin of the Malaysian Mathematical Sciences Society, 43, 3457-3480.
https://doi.org/10.1007/s40840-019-00878-7
[6] Mao, L.X. (2016) Precovers and Preenvelopes by Phantom and Ext-Phantom Morphisms. Communications in Algebra, 44, 1704-1721.
https://doi.org/10.1080/00927872.2015.1027388
[7] Mao, L.X. (2018) Higher Phantom and Ext-Phantom Morphisms. Journal of Algebra and Its Applications, 17, Article 1850012.
https://doi.org/10.1142/S0219498818500123