$\mathscr{X}$-Gorenstein投射模,$\mathscr{X}$-Gorenstein投射维数,$\mathscr{X}$-强n-Gorenstein投射模," /> $\mathscr{X}$-Gorenstein投射模,$\mathscr{X}$-Gorenstein投射维数,$\mathscr{X}$-强n-Gorenstein投射模,"/> $\mathscr{X}$-Gorenstein projective modules,$\mathscr{X}$-Gorenstein projective dimension,$\mathscr{X}$-strongly n-Gorenstein projective modules,"/> <inline-formula><tex-math id="M2">$\mathscr{X}$</tex-math></inline-formula>-strongly <i>n</i>-Gorenstein projective modules

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (8): 26-32, 42.doi: 10.6040/j.issn.1671-9352.0.2022.502

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$\mathscr{X}$-strongly n-Gorenstein projective modules

Cuiping ZHANG(),Wenfei ZHANG*(),Fuxia YANG   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Received:2022-09-16 Online:2023-08-20 Published:2023-07-28
  • Contact: Wenfei ZHANG E-mail:zhangcp@nwnu.edu.cu;ZhangWenFei13@163.com

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Abstract:

Let $\mathscr{X}$ be a class of containing projective modules. In this paper, the concept of the $\mathscr{X}$-strongly n-Gorenstein projective modules is introduced. We give some basic properties and prove that the $\mathscr{X}$-Gorenstein projective dimension of a module M does not exceed a non-negative integer n if and only if M is the direct summand of a $\mathscr{X}$-strongly n-Gorenstein projective module.

Key words: $\mathscr{X}$-Gorenstein projective modules')">$\mathscr{X}$-Gorenstein projective modules, $\mathscr{X}$-Gorenstein projective dimension')">$\mathscr{X}$-Gorenstein projective dimension, $\mathscr{X}$-strongly n-Gorenstein projective modules')">$\mathscr{X}$-strongly n-Gorenstein projective modules

CLC Number: 

  • O153.3
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