吉林大学学报(理学版) ›› 2024, Vol. 62 ›› Issue (3): 515-520.

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Frobenius扩张下的PGFFIn-模与GorensteinFIn-平坦模

樊甲梅, 白洁, 赵仁育   

  1. 西北师范大学 数学与统计学院, 兰州 730070
  • 收稿日期:2023-07-18 出版日期:2024-05-26 发布日期:2024-05-26
  • 通讯作者: 赵仁育 E-mail:zhaory@nwnu.edu.cn

PGFFIn-Modules and Gorenstein FIn-Flat Modules under Frobenius Extensions

FAN Jiamei, BAI Jie, ZHAO Renyu   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China
  • Received:2023-07-18 Online:2024-05-26 Published:2024-05-26

摘要: 设R S是环的Frobenius扩张, M是一个S-模. 证明如果R S是可分Frobenius扩张, 则SM是投射余可解的GorensteinFIn-平坦模(GorensteinFIn-平坦模)当且仅当RM是投射余可解的GorensteinFIn-平坦模(GorensteinFIn-平坦模).

关键词: Frobenius扩张, 可分Frobenius扩张, 投射余可解的GorensteinFIn-平坦模, GorensteinFIn-平坦模

Abstract: Let R S be a Frobenius extension of rings and M be an S-module. We prove that if R S is a separable Frobenius extension, then SM is a projectively coresolved GorensteinFIn-flat module (GorensteinFIn-flat module) if and only if RM is a projectively coresolved GorensteinFIn-flat module (GorensteinFIn-flat module).

Key words:  , Frobenius extension, separable Frobenius extension, projectively coresolved GorensteinFIn-flat , module,  ,  , GorensteinFIn-flat module

中图分类号: 

  • O153.3