拟Frobenius扩张和Ding投射模
Quasi Frobenius Extensions and Ding Projective Modules
廖杨1
作者信息
- 1. 重庆师范大学数学科学学院,重庆沙坪坝 401331
- 折叠
摘要
设R,S是环,R CS是拟Frobenius扩张.为了研究Ding投射模及其维数在拟Frobenius扩张下的同调不变性,对Ding投射模M作张量积,证得M是Ding投射左R-模当且仅当S(⊕)RM是Ding投射左S-模.若RCS是可分拟Frobenius扩张,则M与S(⊕)RM是等价的Ding投射左S-模,且对任意左S-模M,Dpds(M)=DpdR(M).并且在可分拟Frobenius扩张下,环的Ding投射整体维数也具有不变性.
Abstract
Let R and S be rings,R⊂S be a quasi Frobenius extension.In order to study the homological invariances of Ding projective modules and dimensions under quasi Frobenius extensions,making a tensor product on a Ding projective module M,it is proved that M is a Ding projective left R-module if and only if S(⊕)RM is a Ding projective left S-module;If R ⊂S is a separable quasi Frobenius extension,then M and S(⊕)RM are an equivalent Ding projective left S-module,and for any left S-moduleM,DpdS(M)=DpdR(M).And the Ding projective global dimensions of rings also have invariance under a separable quasi Frobenius extension.
关键词
拟Frobenius扩张/Ding投射模/可分扩张Key words
quasi Frobenius extension/Ding projective module/separable extension引用本文复制引用
出版年
2024
NETL
NSTL
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