Frobenius扩张上的Ding投射模

doi:10.6040/j.issn.1671-9352.0.2018.756

《山东大学学报(理学版)》 ›› 2019, Vol. 54 ›› Issue (12): 74-78.doi: 10.6040/j.issn.1671-9352.0.2018.756

Frobenius扩张上的Ding投射模

王占平,张睿杰^*

西北师范大学数学与统计学院, 甘肃兰州 730070

发布日期:2019-12-11
作者简介:王占平(1978— ),女,教授,硕士生导师,研究方向为环的同调理论. E-mail:359220363@qq.com*通信作者简介:张睿杰(1993— ),男,硕士研究生,研究方向为环的同调理论. E-mail:936295823@qq.com
基金资助:
国家自然科学基金资助项目(11561061)

Ding projective modules over Frobenius extensions

WANG Zhan-ping, ZHANG Rui-jie^*

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China

Published:2019-12-11

摘要/Abstract

摘要： 研究了Frobenius扩张上的Ding投射模和Ding投射维数。设R⊂A是可分Frobenius扩张,M是任意左A-模,证明了:M是Ding投射左A-模当且仅当M是Ding投射左R-模当且仅当A⊗_RM和HomR(A,M)是Ding投射左A-模。进一步,得到了关于Ding投射维数的结论。

关键词: Frobenius扩张, Ding投射模, Ding投射维数

Abstract: Ding projective modules over Frobenius extensions and Ding projective dimensions are investigated. Let R⊂A be a separable Frobenius extension, and let M be any left A-module. It is proved that M is a Ding projective left A-module if and only if M is Ding projective left R-module if and only if A_RM and HomR(A,M) are Ding projective left A-modules. Some the conclusion on Ding projective Dimensions are obtained.

Key words: Frobenius extensions, Ding projective modules, Ding projective dimensions

中图分类号:

O153.3

王占平,张睿杰. Frobenius扩张上的Ding投射模[J]. 《山东大学学报(理学版)》, 2019, 54(12): 74-78.

WANG Zhan-ping, ZHANG Rui-jie. Ding projective modules over Frobenius extensions[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(12): 74-78.

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Frobenius扩张上的Ding投射模

Ding projective modules over Frobenius extensions

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