The Localization of Commutative Rings and Localization of Their Modules

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。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.