论文标题
美元
$(\mathcal{F},\mathcal{A})$-Gorenstein flat homological dimensions
论文作者
论文摘要
在本文中，我们开发了$（\ MATHCAL {l}，\ MATHCAL {a}）$ - GORENSTEIN FLAT $ R $ -MODULES $ \ MATHCAL {GF} _ {（\ MATHCAL {F}（f}（r），\ Mathcal {a a} $ quass）的同源属性。其中$ \ Mathcal {a} \ subseteq \ mathrm {mod}（r^{op}）$有时对应于双重对应$（\ Mathcal {l}，\ Mathcal {a}）$。我们研究了$ \ Mathcal {gf} _ {（\ Mathcal {f}（r），\ Mathcal {a}）$带来的薄弱全球和有限维度$ \ mathrm {mod}（r^{op}）\ times \ times \ mathrm {mod}（r）$ by class $ \ mathcal {gf} _ {（\ mathcal {f}（r^{op}）（r^{op}） \ Mathcal {gf} _ {（\ Mathcal {f}（r），\ Mathcal {a}）} $。当双重性对为$（\ Mathcal {f}（r），\ Mathcal {fp} Inj（r^{op}））$，我们在ding-chen环上恢复了G. Yang的结果，我们看到这是$（\ Mathrm {lev}（lev}（lev}（r），\ Mathrm^$ rm rm^ac}）的新事物。
In this paper we develop the homological properties of the $(\mathcal{L}, \mathcal{A})$-Gorenstein flat $R$-modules $\mathcal{GF}_{(\mathcal{F}(R), \mathcal{A})}$ proposed by Gillespie. Where the class $\mathcal{A} \subseteq \mathrm{Mod} (R^{op})$ sometimes corresponds to a duality pair $(\mathcal{L}, \mathcal{A})$. We study the weak global and finitistic dimensions that comes with $\mathcal{GF}_{(\mathcal{F}(R), \mathcal{A})}$ and show that over a $(\mathcal{L}, \mathcal{A})$-Gorenstein ring, the functor $-\otimes _R -$ is left balanced over $\mathrm{Mod} (R^{op}) \times \mathrm{Mod} (R)$ by the classes $\mathcal{GF}_{(\mathcal{F}(R^{op}), \mathcal{A})} \times \mathcal{GF}_{(\mathcal{F}(R), \mathcal{A})}$. When the duality pair is $(\mathcal{F} (R), \mathcal{FP}Inj (R^{op}))$ we recover the G. Yang's result over a Ding-Chen ring, and we see that is new for $(\mathrm{Lev} (R), \mathrm{AC} (R^{op}))$ among others.
