Frobenius扩张下的PGFFIn-模与GorensteinFIn-平坦模

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

Frobenius扩张下的PGF_FIn-模与GorensteinFI_n-平坦模

樊甲梅, 白洁, 赵仁育

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

PGF_FIn-Modules and Gorenstein FI_n-Flat Modules under Frobenius Extensions

FAN Jiamei, BAI Jie, ZHAO Renyu

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/Abstract

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GorensteinFI_n-平坦模（GorensteinFI_n-平坦模)当且仅当_RM是投射余可解的GorensteinFI_n-平坦模(GorensteinFI_n-平坦模).

关键词: Frobenius扩张, 可分Frobenius扩张, 投射余可解的GorensteinFI_n-平坦模, GorensteinFI_n-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 GorensteinFI_n-flat module (GorensteinFI_n-flat module) if and only if _RM is a projectively coresolved GorensteinFI_n-flat module (GorensteinFI_n-flat module).

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

中图分类号:

O153.3

樊甲梅, 白洁, 赵仁育. Frobenius扩张下的PGF_FIn-模与GorensteinFI_n-平坦模[J]. 吉林大学学报(理学版), 2024, 62(3): 515-520.

FAN Jiamei, BAI Jie, ZHAO Renyu. PGF_FIn-Modules and Gorenstein FI_n-Flat Modules under Frobenius Extensions[J]. Journal of Jilin University Science Edition, 2024, 62(3): 515-520.