Journal of Jilin University Science Edition ›› 2022, Vol. 60 ›› Issue (6): 1308-1316.

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Semi-regular Flat Modules over Strong Prüfer Rings

ZHANG Xiaolei1, DAI Guocheng2, XIAO Xuelian3, QI Wei1   

  1. 1. School of Mathematics and Statistics, Shandong University of Technology, Zibo 255049, Shandong Province, China;
    2. School of Mathematical Sciences, Sichuan Normal University, Chengdu 610066, China;
    3. School of Mathematics, Aba Teachers University, Wenchuan 623002, Sichuan Province, China
  • Received:2022-03-13 Online:2022-11-26 Published:2022-11-26

Abstract: 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.

Key words: semi-regular flat module, DQ ring, strong Prüfer ring, semi-regular coherent ring

CLC Number: 

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