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
[1] ENOCHS E E, JENDA O M G. Relative homological algebra[M]. Walter de Gruyter and Co. Berlin:[s.n.] , 2000.
[2] CHEN Jianlong, DING Nanqing. On n-coherent rings[J]. Comm Algebra, 1996, 24(1):3211-3216.
[3] LU Bo, LIU Zhongkui. IFP-flat modules and IFP-injective modules[J]. Comm Algebra, 2012, 40(2):361-374.
[4] UDHAYAKUMAR R. n-IFP-flat modules and n-IFP-injective modules[J]. Asian-Eur J Math, 2017, 10(1):1750014.
[5] ENOCHS E E, JENDA O M G. Copure injective modules[J]. Quaest Math, 1991, 14(1):401-409.
[6] YANG Xiaoyan, LIU Zhongkui. n-flat and n-FP-injective modules[J]. Czechoslovak Math J, 2011, 61(2):359-369.
[7] HERMANN M, IKEDA S, ORBANZ U. Equimultiplicity and blowing up[M]. Berlin: Springer-Verlag, 1988.
[8] ASENSIO M J, LÓPEZ-RAMOS J A, TORRECILLAS B. Gorenstein gr-injective and gr-projective modules[J]. Comm Algebra, 1998, 26(1):225-240.
[9] ASENSIO M J, LÓPEZ-RAMOS J A, TORRECILLAS B. FP-gr-injective modules and gr-FC rings[M] // Algebra and number Theory, 1-11, Lecture Notes in Pure and Appl Math. New York: Dekker, 2000.
[10] ZHAO Tiwei, GAO Zenghui, HUANG Zhaoyong. Relative FP-gr-injective and gr-flat modules[J]. Internat J Algebra Comput, 2010, 28(6):959-977.
[11] GARCÍA ROZAS J R, LÓPES-RAMOS J A, TORRECILLAS B. On the existence of at covers in R-gr[J]. Comm Algebra, 2001, 29(1):3341-3349.
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