JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (11): 48-53.doi: 10.6040/j.issn.1671-9352.0.2023.498

Previous Articles    

FI-injective N-complexes

HAN Xia, LU Bo*   

  1. College of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, Gansu, China
  • Published:2025-11-11

PDF (PC)

48

Abstract: Let n be an integer. The notion of FI-injective N-complexes is introduced and studied. It is proven that an N-complex I is FI-injective over a coherent ring if and only if each In is an FI-injective module and HomR(G,I) is N-exact whenever G is an FP-injective N-complex. The characterization of FI-injective N-complexes is given, and the relationship between it and injective N-complexes is considered.

Key words: injective N-complex, FP-injective N-complex, FI-injective N-complex

CLC Number: 

  • O153.3
[1] MAO Lixin, DING Nanqing. FI-injective and FI-flat modules[J]. Journal of Algebra, 2007, 309(1):367-385.
[2] 唐超. FI-内射复形与FI-平坦复形[D]. 长沙:湖南师范大学,2011. TANG Chao. FI-injective complexes and FI-flat complexes[D]. Changsha: Hunan Normal University, 2011.
[3] 辛大伟,田雪. FI-内射复形[J]. 阜阳师范学院学报(自然科学版),2016,33(2):1-3. XIN Dawei, TIAN Xue. FI-injective complexes[J]. Journal of Fuyang Normal University(Natural Science), 2016, 33(2):1-3.
[4] IYAMA O, KATO K, MIYACHI J. Derived categories of N-complexes[J]. Journal of the London Mathematical Society, 2017, 96(3):687-716.
[5] YANG Xiaoyan, DING Nanqing. The homotopy category and derived category of N-complexes[J]. Journal of Algebra, 2015, 426:430-476.
[6] STENSTRÖM B. Coherent rings and FP-injective modules[J]. Journal of the London Mathematical Society, 1970, 2(2):323-329.
[7] ENOCHS E E, ROZAS J R G. Flat covers of complexes[J]. Journal of Algebra, 1998, 210(1):86-102.
[8] YANG Xiaoyan, LIU Zhongkui. FP-injective complexes[J]. Communications in Algebra, 2009, 38(1):131-142.
[9] LU Bo. FP-injective objects in the category of N-complexes[J]. Indian Journal of Pure and Applied Mathematics, 2024, 55(1):242-255.
[10] YANG Xiaoyan, GAO Tianya. Cotorsion pairs in CN(R)[J]. Algebra Colloquium, 2017, 24(4):577-602.
[1] Yuru CUI,Yang CHENG. A kind of generalization of fine rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(6): 84-90.
[2] Jie WANG,Wenjing CHEN. On w-FPn-projective modules [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(6): 64-70.
[3] Wenjing CHEN,Wen GAO. Gorenstein FP-injective modules over Morita rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(4): 9-15.
[4] Liu ZHOU,Lei QIAO,Dan ZHAO. On w-IFP-flat modules and w-IFP-injective modules [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(2): 22-31.
[5] Dong SU. The module algebra structures of dihedral groups on the full matrix algebra of 2×2 [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(2): 14-21, 31.
[6] Cuiping ZHANG,Jiaojiao DONG,Yinyin YANG. Gorenstein FP-injective dimensions over formal triangular matrix rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(2): 8-13.
[7] Yao WANG,Xin LI,Yanli REN. *-zip rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(2): 1-7.
[8] Hua SUN,Jian ZOU,Ruju ZHAO. Automorphism group of Green algebra of 8-dimensional Radford Hopf algebra [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(11): 61-70.
[9] Longjiao YANG,Hailou YAO. Gorenstein weak projective comodules over a coalgebra [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(8): 43-47, 56.
[10] Cuiping ZHANG,Wenfei ZHANG,Fuxia YANG. $\mathscr{X}$-strongly n-Gorenstein projective modules [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(8): 26-32, 42.
[11] Xianhong YANG,Guoliang TANG,Zhenxing DI. Recollements of Gorenstein flat cotorsion modules over triangular matrix rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(8): 18-25.
[12] Mengge GUAN,Hainan ZHOU,Junchao WEI. Some equivalent characterizations on EP elements [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(8): 13-17.
[13] Yao WANG,Jianghuan CHEN,Yanli REN. Quasi-J-clean rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(6): 1-8.
[14] YIN Jun-qi, YANG Gang. Gorenstein DG-injective complexes [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(10): 28-33.
[15] ZHAO Tiao, ZHANG Chao. q-Cartan matrices of self-injective Nakayama algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(10): 46-51.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd