Some Notes on the Recollements and Weak Global Dimension

To study homological dimensions, the finiteness of the weak global dimension of algebras was investigated by the theory of recollements. Assume that (D(Mod B), D(Mod A), D(Mod C)) is a standard recollement of derived categories. Results show that if the standard recollements satisfy some conditions, then the weak global dimension of the algebra A is finite if and only if so are the algebras B and C. As an application, results show that the finiteness of the weak global dimension of an algebra is invariant under derived equivalent.