拟Frobenius扩张和Ding投射模  

Quasi Frobenius Extensions and Ding Projective Modules

作　　者：廖杨 LIAO Yang(College of Mathematical Science,Chongqing Normal University,Shapingba401331,Chongqing)

机构地区：[1]重庆师范大学数学科学学院,重庆沙坪坝401331

出　　处：《商洛学院学报》2024年第6期35-38,44,共5页Journal of Shangluo University

基　　金：重庆市自然科学基金项目(cstc2021jcyj-msxmX0048)。

摘　　要：设R,S是环,R■S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R■S是可分拟Frobenius扩张,则M与S■_(R)M是等价的Ding投射左S-模,且对任意左S-模M,Dpd_(S)(M)=Dpd_(R)(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。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■_(R)M is a Ding projective left S-module;If R■S is a separable quasi Frobenius extension,then M and S■_(R)M are an equivalent Ding projective left S-module,and for any left S-module M,Dpd_(S)(M)=Dpd_(R)(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 

分 类 号：O154[理学—数学]