JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (6): 71-75.doi: 10.6040/j.issn.1671-9352.0.2022.652

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n-copure Gorenstein AC modules

GAO Nana, YANG Gang*   

  1. School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China
  • Published:2024-06-17

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Abstract: Let R be a ring, n a fixed nonnegative integer and G In(resp., G Fn)the class of all left(resp., right)R-modules of Gorenstein AC injective(resp., Gorenstein AC flat)dimension at most n. A left R-module M(resp., right R-module M)is called n-copure Gorenstein AC injective(resp., n-copure Gorenstein AC flat)if Ext1R(N,M)=0(resp., TorR1(M,N)=0)for any N∈G In. It is proven that a finitely presented right R-module M is n-copure Gorenstein AC flat if and only if M is a cokernel of a G Fn-preenvelope K→F of a right R-module K with F flat.

Key words: n-copure Gorenstein AC-injective module, n-copure Gorenstein AC-flat module, G Fn-preenvelope

CLC Number: 

  • O154.2
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