JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (8): 105-110.doi: 10.6040/j.issn.1671-9352.0.2021.160

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PGF-modules and strongly semi-Gorenstein-projective modules

BAI Jiu-hong, LIANG Li*   

  1. School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China
  • Published:2021-08-09

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Abstract: Let SSGP denote the class of all strongly semi-Gorenstein-projective modules. Some relations between PGF-modules and strongly semi-Gorenstein-projective modules are given, and over an arbitrary ring R, SSGP∩PGF^~=PGF is proved. It is got that SSGP=PGF if and only if SSGP⊆PGF^~, where PGF is the class of all PGF-modules, and PGF^~ is the class of all R-modules with finite PGF-dimension. Finally, the finitistic PGF-dimension of a ring R is equal to the finitistic projective dimension is proved.

Key words: PGF-module, strongly semi-Gorenstein-projective module, finitistic PGF-dimension, finitistic projective dimension

CLC Number: 

  • O154.2
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