JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (2): 63-71.doi: 10.6040/j.issn.1671-9352.0.2021.660

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(n,m)-Strongly projectively coresolved Gorenstein flat modules

ZHONG Kui-chen, ZHANG Cui-ping*, QIN Jun-xia   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2023-02-12

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Abstract: The concept of an (n,m)-strongly projectively coresolved Gorenstein flat module(i.e.(n,m)-strongly PGF module)is introduced, and some basic properties of it are given. It is proved that if M is an (n,m)-strongly PGF module, then(1)PGF dimension of M PGFd(M)≤m;(2)when 1≤i≤m, the ith syzygy of M is(n,m-i)-strongly PGF module; when i≥m, the ith syzygy of M is(n,0)-strongly PGF module. Secondly, it is proved that the dth syzygy of M is(1,m)-strongly PGF module, then PGF d(M)=k≤d+m, and M is (1,k)-strongly PGF module.

Key words: PGF modules, strongly PGF modules, n-strongly PGF modules, (n,m)-strongly PGF modules

CLC Number: 

  • O153.3
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