JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2018, Vol. 53 ›› Issue (10): 17-21.doi: 10.6040/j.issn.1671-9352.0.2017.576

Previous Articles     Next Articles

Gorenstein homological dimensions of modules under exact zero-divisors

GUO Shou-tao, WANG Zhan-ping   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Received:2017-11-07 Online:2018-10-20 Published:2018-10-09

PDF (PC)

390

Abstract: Let R be a commutative Noetherian ring with identity, x be an exact zero-divisor over R. Gorenstein homological dimensions of modules under exact zero-divisors are investigated. M/xM is Gorenstein projective(injective, flat)R/xR-module if M is Gorenstein projective(injective, flat)R-module, the results of corresponding dimensions are gained. The result can also be obtained for Ding projective(injective)R- modules.

Key words: Gorenstein projective(injective, flat)modules, Gorenstein projective(injective, flat)dimensions, exact zero-divisors

CLC Number: 

  • O154.2
[1] AUSLANDER M, BRIDGER M. Stable module theory[M]. Providence: Memoirs of the American Mathematical Society, 1969: 94.
[2] ENOCHS E E, JENDA O M G. Gorenstein injective and projective modules[J]. Mathematische Zeitschrift, 1995, 220(1):611-633.
[3] ENOCHS E E, JENDA O M G, TORRECILLAS B. Gorenstein flat modules[J]. Journal of Nanjing University-Math, 1993, 1:1-9.
[4] ENOCHS E E, JENDA O M G. Relative homological algebra[M]. Berlin: Walter de Gruyter, 2000.
[5] CHRISTENSEN L W. Gorenstein dimensions[J]. Lecture Notes in Mathematics, 2000, 1747.
[6] HOLM H. Gorenstein homological dimensions[J]. Journal of Pure and Applied Algebra, 2004, 189:167-193.
[7] HENRIQUES I B D A, ??塁EGA L M. Free resolutions over short Gorenstein local rings[J]. Mathematische Zeitschrift, 2010, 267:645-663.
[8] BERGH P A, CELIKBAS O, JORGENSEN D A. Homological algebra modulo exact zero-divisors[J]. Kyoto Journal of Mathematics, 2014, 54:879-895.
[9] DIBAEI M T, GHEIBI M. Sequence of exact zero-divisors[J]. Mathematics, 2011, 12:1-18.
[10] AMANZADEH E, DIBAEI M T. Auslander class, GC, and C-projective modules modulo exact zero-divisors[J]. Communications in Algebra, 2015, 43:4320-4333.
[11] DING Nanqing, LI Yuanlin, MAO Lixin. Strongly Gorenstein flat modules[J]. Journal of Australian Mathematical Society, 2009, 86(3):323-338.
[12] DING Nanqing, MAO Lixin. Gorenstein FP-injective and Gorenstein flat modules[J]. Journal of Algebra and Its Applications, 2008, 7(4):491-506.
[13] GILLESPIE J. Model structures on modules over Ding-Chen rings[J]. Homology Applications, 2010, 12(1):61-73.
[14] CHRISTENSEN L W. Semi-dualizing complexes and their Auslander categories[J]. Transactions of the American Mathematical Society, 2001, 353:1839-1883.
[15] ENOCHS E E, IZURDIAGA M C, TORRECILLAS B. Gorenstein conditions over triangular matrix rings[J]. Journal of Pure and Applied Algebra, 2014, 218:1544-1554.
[16] MAHDOU N, TAMEKKANE M. Strongly n-Gorenstein projective, injective and flat modules[J]. Journal of the Austrilian Mathematical Society, 2013, 87(3):395-407.
[1] CHEN Wen-qian, ZHANG Xiao-jin, ZAN Li-bo. The number of tilting modules over Gorenstein algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(10): 14-16.
[2] . FR-injective and FR-flat dimensions of complexes [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(6): 1-6.
[3] YANG Chun-hua. A note on the Gc-injective dimension of a complex [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(11): 82-86.
[4] LUO Xiao-qiang, XING Jian-min. Ding gr-injective and gr-flat modules [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(11): 87-91.
[5] WANG Xiao-qing, LIANG Li. Strongly cotorsion modules under faithfully flat co-base change [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(11): 92-94.
[6] XU Hui, ZHAO Zhi-bing. Relative torsionless modules [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(8): 75-80.
[7] CHEN Xiu-li, CHEN Jian-long. Homological dimensions with respect to semidualizing modules and excellent extensions [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(8): 85-89.
[8] SUN Wei-kun, LIN Han-xing. Representation dimension of one-point extension algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(6): 85-91.
[9] XIE Zong-zhen, ZHANG Xiao-jin. On algebras with all τ-rigid modules projective [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(2): 16-20.
[10] CHENG Hai-xia, YIN Xiao-bin. Gorenstein injective objects in Abelian categories [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(2): 79-84.
[11] CHEN Xiu-li, CHEN Jian-long. Copure projective dimensions under Hopf extensions [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(10): 7-10.
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