论文标题
通过半双重模块定义的相对EXT组的平衡
The balance of relative Ext groups defined by semi dualizing modules
论文作者
论文摘要
让$ r $为具有身份的通勤赛戒指，每$ r $ $ c $每半教学模块。令$ \ mathscr {p} _c（r）$和$ \ mathscr {i} _c（r）$分别表示$ c $ -projective和$ c $ -c $ -imentive $ r $ -mmodules的类。 We show that their induced Ext bifunctors $\text{Ext}^i_{\mathscr{P}_C}(-,\sim)$ and $\text{Ext}^i_{\mathscr{I}_C}(-,\sim)$ coincide for all $i\geq 0$ if and only if $C$ is projective.另外，我们通过使用一些特殊的Cotorsion理论为$ c $提供了一些其他标准。
Let $R$ be a commutative Noetherian ring with identity and $C$ a semidualizing module for $R$. Let $\mathscr{P}_C(R)$ and $\mathscr{I}_C (R)$ denote, respectively, the classes of $C$-projective and $C$-injective $R$-modules. We show that their induced Ext bifunctors $\text{Ext}^i_{\mathscr{P}_C}(-,\sim)$ and $\text{Ext}^i_{\mathscr{I}_C}(-,\sim)$ coincide for all $i\geq 0$ if and only if $C$ is projective. Also, we provide some other criteria for $C$ to be projective by using some special cotorsion theories.
