对偶数环导出范畴的Recollements

Recollements of Derived Categories of Rings of Dual Numbers

设A,A_1和A_2是环.证明若环A的上有界导出范畴D^-(A)允许有关于环A_1和A_2的上有界导出范畴D^-(A_1)和D^-(A_2)的recollement,则A的对偶数环A[ε]的上有界导出范畴D^-(A[ε])允许有关于A_1的对偶数环的上有界导出范畴D^-(A_1[ε])和A_2的对偶数环的上有界导出范畴D^-(A_2[ε])的recollement.

Let A,A 1 and A 2 be rings.It is proved that,if the upper bounded derived module category D^-(A-Mod)admits a recollement relative to D^-(A 1-Mod)and D^-(A 2-Mod),then D^-(A[ε]-Mod)admits a recollement relative to D^-(A 1[ε]-Mod)and D^-(A 2[ε]-Mod),where A[ε]is the ring of dual number of ring A.