JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (2): 99-103.doi: 10.6040/j.issn.1671-9352.0.2019.138

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n-IFP-gr-injective modules and n-IFP-gr-flat modules

ZHAO Jun-xiu, DI Rong-rong, DI Zhen-xing*   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2020-02-14

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Abstract: The notions of n-IFP-graded injective modules and n-IFP-graded flat modules are introduced and investigated, where n is a positive integer. It proves that both(gr-I Fn, gr-I In)and(gr-I In, gr-I Fn)form two duality pairs over any graded ring R, where gr-I Fn denotes the class of all n-IFP-graded flat right R-modules and gr-I In denotes the class of all n-IFP-graded injective left R-modules. As applications, it shows that every graded right R-module has a gr-I Fn-preenvelope, every graded left R-module has a gr-I In-cover, and(gr-I Fn, gr-I F ⊥n)forms a perfect cotorsion pair.

Key words: n-IFP-gr-injective module, n-IFP-gr-flat module, duality pair, preenvelope, cover, cotorsion pair

CLC Number: 

  • O153.3
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