Cograde Conditions and Cotorsion Pairs
Cograde Conditions and Cotorsion Pairs
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DOI：
10.4171/prims/56-3-2
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发表时间：
2019-07
影响因子：
1.2
通讯作者：
Xi Tang;Zhaoyong Huang
中科院分区：
文献类型：
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作者：
Xi Tang;Zhaoyong Huang
设$R$和$S$是环，$_R\omega_S$是半对偶双模.利用模的（强）余度条件研究了二重函子$\Tor^S_i（\omega，\Ext^i_{R}（\omega，-））$保持满态和二重函子$\Ext_{R}^i（\omega，\Tor_i^{S}（\omega，-））$保持单态的条件.在一定的模共度条件下，构造了两个完备的余挠对。此外，我们还建立了环的某些相对有限维数与$\omega$的左右投射维数之间的关系。
Let $R$ and $S$ be rings and $_R\omega_S$ a semidualizing bimodule. We study when the double functor $\Tor^S_i(\omega, \Ext^i_{R}(\omega,-))$ preserves epimorphisms and the double functor $\Ext_{R}^i(\omega, \Tor_i^{S}(\omega,-))$ preserves monomorphisms in terms of the (strong) cograde conditions of modules. Under certain cograde condition of modules, we construct two complete cotorsion pairs. In addition, we establish the relation between some relative finitistic dimensions of rings and the right and left projective dimensions of $\omega$.