JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2022, Vol. 57 ›› Issue (2): 31-37.doi: 10.6040/j.issn.1671-9352.0.2021.061

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n-Gorenstein graded projective(injective)modules

YUAN Qian1, ZHANG Wen-hui1*, ZHANG Ming2   

  1. 1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China;
    2. Longgang Middle School, Dazu District, Chongqing 402360, China
  • Published:2022-01-07

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Abstract: Let G be a multiplicative group, R be a G-graded ring, n-Gorenstein graded projective and n-Gorenstein graded injective modules are introduced, the homological properties and the dimensions of the two types of modules are investigated. It is proved that if the graded R-module M satisfies n-G-gr-pdRM=m<∞, then exists an exact sequence 0→K→G→M→ 0, where G is n-Gorenstein graded projective R-module and pdRK=m-1.

Key words: graded ring, n-Gorenstein graded projective(injective)module, n-Gorenstein graded projective(injective)dimension

CLC Number: 

  • O153.3
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