JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (8): 18-25.doi: 10.6040/j.issn.1671-9352.0.2022.318

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Recollements of Gorenstein flat cotorsion modules over triangular matrix rings

Xianhong YANG(),Guoliang TANG,Zhenxing DI*()   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Received:2022-05-30 Online:2023-08-20 Published:2023-07-28
  • Contact: Zhenxing DI E-mail:yxh210805@163.com;dizhenxing19841111@126.com

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Abstract:

Let $\mathit{\boldsymbol{T}} = \left( {\begin{array}{*{20}{c}} A&0\ U&B \end{array}} \right)$ be a triangular matrix ring, where A and B are rings and U is a (B, A)-bimodule. The equivalent characterization of Gorenstein flat cotorsion modules in the category of left T-modules is given. With the help of the above result, it is proved that when ring A and bimodule U satisfy some conditions, there is a left recollement of the stable category of Gorenstein flat cotorsion T-module category. Under stronger conditions, a recollement of this stable category is further obtained.

Key words: triangular matrix ring, Gorenstein flat cotorsion module, recollement of a triangulated category

CLC Number: 

  • O153.3
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