强Prüfer环上的半正则平坦模  

Semi-regular Flat Modules over Strong Prüfer Rings

作　　者：张晓磊 戴国成 肖雪莲 齐薇 ZHANG Xiaolei;DAI Guocheng;XIAO Xuelian;QI Wei(School of Mathematics and Statistics,Shandong University of Technology,Zibo 255049,Shandong Province,China;School of Mathematical Sciences,Sichuan Normal University,Chengdu 610066,China;School of Mathematics,Aba Teachers University,Wenchuan 623002,Sichuan Province,China)

机构地区：[1]山东理工大学数学与统计学院,山东淄博255049 [2]四川师范大学数学科学学院,成都610066 [3]阿坝师范学院数学学院,四川汶川623002

出　　处：《吉林大学学报（理学版）》2022年第6期1308-1316,共9页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11901412,12061001,12201361).

摘　　要：利用半正则余平坦模刻画强Prüfer环,即证明环R是强Prüfer环当且仅当R的任意理想都是半正则平坦模,当且仅当半正则平坦模的任意子模都是半正则平坦模,当且仅当任意[KG*8]R-模都有满的半正则平坦包.We characterized strong Prüfer rings by using semi-regular flat modules.Namely,we proved that a ring R was strong Prüfer if and only if any ideal of R was semi-regular flat module,if and only if any submodule of a semi-regular flat module was semi-regular flat module,if and only if any R-module had an epimorphic semi-regular flat envelope.

关 键 词：半正则平坦模 DQ环 强Prüfer环 半正则凝聚环 

分 类 号：O154[理学—数学]