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     Next Articles

On w-FPn-projective modules

Jie WANG(),Wenjing CHEN*()   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Received:2022-12-27 Online:2024-06-20 Published:2024-06-17
  • Contact: Wenjing CHEN E-mail:18394482624@163.com;chenwj@nwnu.edu.cn

RichHTML

0

PDF (PC)

390

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.
doi: 10.1080/00927879408825061
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.
doi: 10.3969/j.issn.1000-5277.2003.04.003
ZHOU Dexu . Some characterizations of n-coherent rings[J]. Journal of Fujian Normal University (Natural Science), 2003, 19 (4): 9- 12.
doi: 10.3969/j.issn.1000-5277.2003.04.003
4 BRAVO D , PÉREZ M A . Finiteness conditions and cotorsion pairs[J]. Journal of Pure and Applied Algebra, 2017, 221 (6): 1249- 1267.
doi: 10.1016/j.jpaa.2016.09.008
5 WANG F G , MCCASLAND R L . On w-modules over strong Mori domains[J]. Communications in Algebra, 1997, 25 (4): 1285- 1306.
doi: 10.1080/00927879708825920
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.
doi: 10.4134/JKMS.2011.48.1.207
7 WANG F G , KIM H . Relative FP-injective modules and relative IF rings[J]. Communications in Algebra, 2021, 49 (8): 3552- 3582.
doi: 10.1080/00927872.2021.1900861
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.
doi: 10.1080/00927879908826483
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] CUI Yuru, CHENG Yang. A kind of generalization of fine rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(6): 84-90.
[2] Wenjing CHEN,Wen GAO. Gorenstein FP-injective modules over Morita rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(4): 9-15.
[3] 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.
[4] 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.
[5] 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.
[6] Yao WANG,Xin LI,Yanli REN. *-zip rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(2): 1-7.
[7] 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.
[8] Longjiao YANG,Hailou YAO. Gorenstein weak projective comodules over a coalgebra [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(8): 43-47, 56.
[9] 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.
[10] 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.
[11] Mengge GUAN,Hainan ZHOU,Junchao WEI. Some equivalent characterizations on EP elements [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(8): 13-17.
[12] Yao WANG,Jianghuan CHEN,Yanli REN. Quasi-J-clean rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(6): 1-8.
[13] YIN Jun-qi, YANG Gang. Gorenstein DG-injective complexes [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(10): 28-33.
[14] ZHAO Tiao, ZHANG Chao. q-Cartan matrices of self-injective Nakayama algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(10): 46-51.
[15] 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.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
[1] QI Ying-hua,QI Ai-qin . Periodic boundary value problems for differential equations with arguments[J]. J4, 2007, 42(7): 66 -71 .
[2] LI Meng-qiao, ZHAO Xian-feng*, SHU Yong-lu. Supercyclic subspace of a separable Banach space[J]. J4, 2012, 47(10): 102 -104 .
[3] DONG Ai-Jun, LI Guo-Jun, JU Jing-Song. List edge and list total colorings of planar graphs with adjacent triangles[J]. J4, 2009, 44(10): 17 -20 .
[4] LIU Tian-bao,LI Zong-bao,PENG yan-fen, . Relationships between the anesthetic activities for Arenicola larva and the structures of organic molecules[J]. J4, 2006, 41(6): 129 -131 .
[5] LIU Qian-hui1, PEI Hai-yan1, 2,*, HU Wen-rong1,2, XIE Jun3. Population characteristics and seasonal variations of  phytoplankton in Nansi Lake[J]. J4, 2010, 45(5): 12 -18 .
[6] WANG Tao . Pointwise approximation of Post-Gamma operators for functions with locally bounded derivatives[J]. J4, 2007, 42(4): 75 -78 .
[7] LIU Jia-guo . The complex modulus and the complex compliance for higher-order fractional constitutive models of visco-elastic materials[J]. J4, 2008, 43(4): 85 -88 .
[8] LEI Xue-ping. Almost complete C-tilting modules[J]. J4, 2011, 46(2): 101 -104 .
[9] XU Tu-lan . A.D.I. Galerkin method for a nonlinear hyperbolic differential system[J]. J4, 2006, 41(4): 20 -24 .
[10] YANG Shi-zhou1, SONG Xue-mei2. Quasi-McCoy rings relative to a monoid[J]. J4, 2010, 45(8): 47 -52 .
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd