模范畴Recollement的Koenig定理

Koenig's Theorem of Recollement of Module Categories

Koenig定理描述了环的导出范畴允许recollement的一个充分必要条件.本文给出环的模范畴版本的Koenig定理及其应用.应用一是可以导出Morita等价定理,应用二是可以描述三角矩阵环与模范畴的recollement之间的密切联系.

Koenig＇s theorem describes a necessary and sufficient criterion for the existence of a recollement of derived categories of rings.This paper gives Koenig＇s theorem for the version of a recollement of module categories of rings.As two applications,we give a new proof of Morita＇s equivalent theorem and describe the close relation between a triangular matrix ring and a recollement of module categories of rings.