JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (8): 1-5.doi: 10.6040/j.issn.1671-9352.0.2021.332

   

Pure projective dimensions on recollements of Abelian categories

YAN Mei-qi, YAO Hai-lou*   

  1. College of Mathematics, Faculty of Science, Beijing University of Technology, Beijing 100124, China
  • Published:2021-08-09

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Abstract: The concepts of pure projective dimensions in Abelian categories are introduced. Let Rab(A,B,C )be a recollement of Abelian categories where A,B and C are Abelian categories, the relations of pure projective objects and pure projective dimensions of objects in three Abelian categories are studied. As applications, the pure projective modules and pure projective dimensions over formal triangular matrix rings are studied. Finally, it is proved that pure projective dimension of B is finite if and only if the pure projective dimensions of A and C are finite under some conditions.

Key words: recollement, Abelian category, pure projective dimension

CLC Number: 

  • O153.3
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[2] CHEN Xiu-li, CHEN Jian-long. Copure projective dimensions under Hopf extensions [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(10): 7-10.
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