交换环的局部化及其模的局部化
The Localization of Commutative Rings and Localization of Their Modules
摘要: 本论文对于交换环及其模，给出了局部化的定义，讨论了在该定义下局部化的若干性质，同时根据交换环的局部化研究了交换半环的局部化的相关性质，得到了一些有趣的新结果。对于开阔读者的视野，以及进一步研究交换环性质有一定的启发作用，相信在一些领域会有一定的应用。
Abstract: This paper gives the definition of localization for commutative rings and their modules, discusses several properties of localization under this definition, and at the same time, studies the related properties of the localization of commutative semirings based on the localization of commutative rings, and obtains some interesting new results. It has a certain inspiring effect on broadening the readers’ horizons and further studying the properties of commutative rings, and it is believed that it will have certain applications in some fields.
文章引用：陈洪楠. 交换环的局部化及其模的局部化[J]. 运筹与模糊学, 2025, 15(2): 198-205. https://doi.org/10.12677/orf.2025.152076

参考文献

[1] Anderson, F.W. and Fuller, K.R. (1992) Rings and Categories of Modules. 2nd Edition, Graduate Texts in Mathematics, Springer-Verlag. [Google Scholar] [CrossRef] 
[2] Pan, Y. and Wei, J.C. (2015) Several Equivalent Characterizations of CN Rings. The College Mathematics Journal, 31, 99-104.
[3] Pinter-Lucke, J. (2007) Commutativity Conditions for Rings: 1950-2005. Expositiones Mathematicae, 25, 165-174. [Google Scholar] [CrossRef] 
[4] Abdollahi, A., Bell, H.E. and Klein, A.A. (2007) On Commutativity and Centrality in Infinite Rings. Communications in Algebra, 35, 1323-1332. [Google Scholar] [CrossRef] 
[5] Andima, S. and Pajoohesh, H. (2010) Commutativity of Rings with Derivations. Acta Mathematica Hungarica, 128, 1-14. [Google Scholar] [CrossRef] 
[6] Ashraf, M. and Wani, B.A. (2019) On Commutativity of Rings and Banach Algebras with Generalized Derivations. Advances in Pure and Applied Mathematics, 10, 155-163. [Google Scholar] [CrossRef] 
[7] Ligh, S. and Richoux, A. (1977) A Commutativity Theorem for Rings. Bulletin of the Australian Mathematical Society, 16, 75-77. [Google Scholar] [CrossRef] 
[8] Wei, J. (2014) Some Notes on CN Rings. Bulletin of the Malaysian Mathematical Sciences Society, 38, 1589-1599. [Google Scholar] [CrossRef] 
[9] Wei, J. and Fan, Z. (2015) A Generalization of Commutativity Theorem for Rings. Annals of the Alexandru Ioan Cuza University-Mathematics, 61, 97-100. [Google Scholar] [CrossRef] 
[10] Yang, Q., Chu, M.Q. and Lu, E.W. (2015) A Note of Commutativity Theorem of Rings. Journal of Nantong University (Natural Science Edition), 14, 69-70, 90.
[11] Du, Q.L. and Sun, J.H. (2014) Right Singular Ideals and Commutativity Theorems for Rings. Journal of Yangzhou University (Natural Science Edition), 17, 5-7.
[12] Bell, H.E. (2017) Commutativity of Rings with Identities on Subsets. Asian-European Journal of Mathematics, 10, Article 1750018. [Google Scholar] [CrossRef] 
[13] 冯克勤. 交换代数基础[M]. 北京: 高等教育出版社, 1986.
[14] 严质彬, 游宏. 交换半环的局部化[J]. 哈尔滨工业大学学报, 2001, 33(6): 732-735.
[15] 王秋丽, 苏业芹. 交换模的广义局部化[J]. 商丘师范学院学报, 2012, 28(12): 19-22.
[16] 苏业芹, 王秋丽. 模的广义局部化及其性质[J]. 商丘师范学院学报, 2013, 29(9): 22-24.
[17] 刘树芳, 唐高华. 交换环的拟准素理想和理想的拟准素分解[J]. 广西师范学院学报(自然科学版), 2007, 24(2): 19-24.
[18] 庞佳. 乘法封闭集的伪局部化与PVMR的刻画[D]: [硕士学位论文]. 成都: 四川师范大学, 2009.

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