模范畴Recollement的Koenig定理

林增强, 王敏雄

数学学报 ›› 2011, Vol. 54 ›› Issue (3) : 461-466.

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数学学报 ›› 2011, Vol. 54 ›› Issue (3) : 461-466. DOI: 10.12386/A2011sxxb0047
论文

模范畴Recollement的Koenig定理

    林增强, 王敏雄
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Koenig’s Theorem of Recollement of Module Categories

    Zeng Qiang LIN, Min Xiong WANG
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摘要

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.  

Abstract

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.  

关键词

模范畴 / recollement / 三角矩阵环

Key words

recollement / module category / triangular matrix ring

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林增强, 王敏雄. 模范畴Recollement的Koenig定理. 数学学报, 2011, 54(3): 461-466 https://doi.org/10.12386/A2011sxxb0047
Zeng Qiang LIN, Min Xiong WANG. Koenig’s Theorem of Recollement of Module Categories. Acta Mathematica Sinica, Chinese Series, 2011, 54(3): 461-466 https://doi.org/10.12386/A2011sxxb0047

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基金

国家自然科学基金资助项目(10671161);华侨大学科研启动基金资助项目(08BS506)

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