$(\Flat, \A)$-Gorenstein flat homological dimensions
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In this paper we develop the homological properties of the Gorenstein $(\Le, \A)$-flat $R$-modules $\GF_{(\Flat (R), \A)}$ proposed by Gillespie, \linebreak where the class $\A \subseteq \Modu (R^{\op})$ sometimes corresponds to a duality pair $(\Le, \A)$. We study the weak global and finitistic dimensions that come with the class $\GF_{(\Flat (R), \A)}$ and show that over a $(\Le, \A)$-Gorenstein ring, the functor $-\otimes _R-$ is left balanced over $\Modu (R^{\op}) \times \Modu (R)$ by the classes $\GF_{(\Flat (R^{\op}), \A)} \times \GF_{(\Flat (R), \A)}$. When the duality pair is $(\Flat (R), \mathcal{FP}Inj (R^{\op}))$ 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.
Abstract
In this paper we develop the homological properties of the Gorenstein $(\Le, \A)$-flat $R$-modules $\GF_{(\Flat (R), \A)}$ proposed by Gillespie, \linebreak where the class $\A \subseteq \Modu (R^{\op})$ sometimes corresponds to a duality pair $(\Le, \A)$. We study the weak global and finitistic dimensions that come with the class $\GF_{(\Flat (R), \A)}$ and show that over a $(\Le, \A)$-Gorenstein ring, the functor $-\otimes _R-$ is left balanced over $\Modu (R^{\op}) \times \Modu (R)$ by the classes $\GF_{(\Flat (R^{\op}), \A)} \times \GF_{(\Flat (R), \A)}$. When the duality pair is $(\Flat (R), \mathcal{FP}Inj (R^{\op}))$ 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.
참고문헌 (27)
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