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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2019; 56(4): 1031-1048

Online first article April 4, 2019      Printed July 1, 2019

https://doi.org/10.4134/JKMS.j180577

Copyright © The Korean Mathematical Society.

The resolution dimensions with respect to balanced pairs in the recollement of abelian categories

Xuerong Fu, Yonggang Hu, Hailou Yao

Heze University; Beijing University of Technology; Beijing University of Technology

Abstract

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In this paper we study recollements of abelian categories and balanced pairs. The main results are: recollements induce new balanced pairs from the middle category; the resolution dimensions are bounded under certain conditions. As an application, the resolution dimensions with respect to cotilting objects of abelian categories involved in recollements are recovered.

Keywords: recollement, resolution dimension, balanced pair

MSC numbers: 16E10, 16E30, 18E10

Supported by: This work was supported by National Natural Science Foundation of China (Grant No. 11671126).

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