JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (6): 64-70.doi: 10.6040/j.issn.1671-9352.0.2022.650

Previous Articles    

On w-FPn-projective modules

WANG Jie, CHEN Wenjing*   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2024-06-17

Abstract: Let n≥1 be an integer or n=∞. The definitions of w-FPn-projective modules and w-FPn-projective dimensions of modules are introduced, and their properties are studied. At the same time, some properties of w-FPn-projective modules over n-coherent rings are discussed.

Key words: w-FPn-projective module, w-FPn-projective dimension, n-cohernet ring

CLC Number: 

  • O153.3
[1] BOURBAKI N. Commutative algebra[M]. Paris: Hermann, 1972.
[2] COSTA D L. Parameterizing families of non-noetherian rings[J]. Communications in Algebra, 1994, 22(10):3997-4011.
[3] 周德旭. n-凝聚环的若干刻划[J]. 福建师范大学学报(自然科学版),2003,19(4):9-12. ZHOU Dexu. Some characterizations of n-coherent rings[J]. Journal of Fujian Normal University(Natural Science), 2003, 19(4):9-12.
[4] BRAVO D, PÉREZ M A. Finiteness conditions and cotorsion pairs[J]. Journal of Pure and Applied Algebra, 2017, 221(6):1249-1267.
[5] WANG F G, MCCASLAND R L. On w-modules over strong Mori domains[J]. Communications in Algebra, 1997, 25(4):1285-1306.
[6] YIN Huayu, WANG Fanggui, ZHU Xiaosheng, et al. w-Modules over commutative rings[J]. Journal of the Korean Mathematical Society, 2011, 48(1):207-222.
[7] WANG F G, KIM H. Relative FP-injective modules and relative IF rings[J]. Communications in Algebra, 2021, 49(8):3552-3582.
[8] KHALED ASSAAD R A, BOUBA E M, TAMEKKANTE M. w-FP-projective modules and dimensions[M] //ASHRAF M, ALI A, DE FILIPPIS V. Algebra and Related Topics with Applications. Singapore: Springer, 2022:47-57.
[9] 宋菲菲. w-FPn-平坦模与w-FPn-内射模的一些研究[D]. 成都:四川师范大学,2022. SONG Feifei. The study of some properties of w-FPn-flat and w-FPn-injective modules[D]. Chengdu: Sichuan Normal University, 2022.
[10] XUE Weimin. On n-presented modules and almost excellent Extensions[J]. Communications in Algebra, 1999, 27(3):1091-1102.
[11] WANG F G, KIM H. Foundations of commutative rings and their modules[M]. Singapore: Springer, 2016.
[12] ENOCHS E E, JENDA O M G. Relative homological algebra[M]. Berlin: Walter De Gruyter, 2000.
[13] 王芳贵,张俊. w-Noether环上的内射模[J]. 数学学报(中文版),2010,53(6):1119-1130. WANG Fanggui, ZHANG Jun. Injective modules over w-noetherian rings[J]. Acta Mathematica(Chinese Series), 2010, 53(6):1119-1130.
[1] Wenjing CHEN,Wen GAO. Gorenstein FP-injective modules over Morita rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(4): 9-15.
[2] 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.
[3] 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.
[4] 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.
[5] Yao WANG,Xin LI,Yanli REN. *-zip rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(2): 1-7.
[6] 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.
[7] Longjiao YANG,Hailou YAO. Gorenstein weak projective comodules over a coalgebra [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(8): 43-47, 56.
[8] 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.
[9] 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.
[10] Mengge GUAN,Hainan ZHOU,Junchao WEI. Some equivalent characterizations on EP elements [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(8): 13-17.
[11] Yao WANG,Jianghuan CHEN,Yanli REN. Quasi-J-clean rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(6): 1-8.
[12] YIN Jun-qi, YANG Gang. Gorenstein DG-injective complexes [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(10): 28-33.
[13] ZHAO Tiao, ZHANG Chao. q-Cartan matrices of self-injective Nakayama algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(10): 46-51.
[14] ZHANG Cui-ping, LIU Ya-juan. Strongly Gorenstein C-injective module and strongly Gorenstein C-flat module [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(10): 24-30.
[15] GUO Hui-ying, ZHANG Cui-ping. Ext-strong Ding projective modules [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(10): 31-36.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!