JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (2): 89-94.doi: 10.6040/j.issn.1671-9352.0.2018.145

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Finitely presented dimensions on recollements of Abelian categories

FENG Yao-yao, YAO Hai-lou*   

  1. College of Applied Sciences, Beijing University of Technology, Beijing 100124, China
  • Published:2019-02-25

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Abstract: The concepts of finitely presented dimensions in Abelian categories are introduced, and the relations of finitely presented dimensions of objects in a short exact sequence are studied. Let Rab(A,B,C )be a recollement of Abelian categories where A,B and C are abelian categories, it is proved that finitely presented dimension of B is finite if and only if the finitely presented dimensions of A and C are finite under some conditions.

Key words: recollement, Abelian category, finitely presented dimension

CLC Number: 

  • O153.3
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