Quasi Frobenius Extensions and Ding Projective Modules
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.
quasi Frobenius extensionDing projective moduleseparable extension
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