JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (4): 60-66.doi: 10.6040/j.issn.1671-9352.0.2018.405

Previous Articles     Next Articles

n-Ding projective and n-Ding injective modules

ZHANG Ming, ZHANG Wen-hui*   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2019-04-08

PDF (PC)

405

Abstract: n-Ding projective and n-Ding injective modules are introduced, the homological properties of these two kinds of modules are discussed, and the hereditary property of the n-Ding projectiveness of module under the excellent extension is investigated.

Key words: n-Ding projective module, n-Ding injective module, n-Ding projective dimension, n-Ding injective dimension

CLC Number: 

  • O153.3
[1] MAO Linxin, DING Nanqing. Gorenstein FP-injective and Gorenstein flat modules[J]. Journal of Algebra and Its Applications, 2008, 7(4):491-506.
[2] GILLESPIE J. Model structures on modules over Ding-Chen rings[J]. Homology, Homotopy and Applications, 2010, 12(1):61-73.
[3] TANG Xi. Applications of n-Gorenstein projective and injective modules[J]. Hacettepe Journal of Mathematics and Statistics, 2015, 44(6):1435-1443.
[4] ENOCHS E E, JENDA O M G. Gorenstein injective and projective modules[J]. Math Z, 1995, 220(4):611-633.
[5] STENSTRÖM B. Coherent rings and FP-injective modules[J]. J London Math Soc(Ser2), 1970, 2:323-329.
[6] HOLM H. Gorenstein homological dimensions[J]. Journal of Pure and Applied Algebra, 2004, 189:167-193.
[7] ENOCHS E E, JENDA O M G. Relative homological algebra[M]. Berlin: Walter de Gruyter, 2000.
[8] HUANG Zhaoyong. Proper resolutions and Gorenstein categories[J]. Journal of Algebra, 2013, 393:142-169.
[9] LAM T Y. Lectures on modules and rings[M] // Graduate Texts in Math. New York: Springer-Verlag, 1999.
[10] ANDERSON F W, FULLER K R. Rings and categories of modules[M]. New York: Springer-Verlag, 1992.
[11] FIELDHOUSE D J. Character modules, dimension and purity[J]. Glasgow Mathematical Journal, 1972, 13(2):144-146.
[12] PASSMAN D S. The algebraic structure of group rings[M]. New York: Wiley-Interscience, 1977.
[13] FANG Hongjin. Normalizing extensions and modules[J]. Journal of Mathematical Research and Exposition, 1992, 12(3):401-406.
[1] WU Xiao-ying, WANG Fang-gui. Graded version of Enochs theorem [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(10): 22-26.
[2] CHENG Cheng, ZOU Shi-jia. Irreducible splitting trace module of a class of Hopf algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(4): 11-15.
[3] ZHU Lin. Separated monic representations of quivers of type A4and RSS equivalences [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(2): 1-8.
[4] GUO Shuang-jian, LI Yi-zheng. When is BHQ a pre-braided category over quasi-Hopf algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(12): 10-15.
[5] LI Jin-lan, LIANG Chun-li. Strongly Gorenstein C-flat modules [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(12): 25-31.
[6] WANG Hui-xing, CUI Jian, CHEN Yi-ning. Nil *-clean rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(12): 16-24.
[7] LU Dao-wei, WANG Zhen. L-R smash product for bialgebroids [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(12): 32-35.
[8] . Gelfand-Krillov dimension of quantized enveloping algebra Uq(An) [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(10): 12-17.
[9] SUN Yan-zhong, YANG Xiao-yan. Gorenstein AC-projective modules with respect to a semidualizing module [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(10): 31-35.
[10] MA Xin, ZHAO You-yi, NIU Xue-na. Homology resolutions and homological dimensions of complexes [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(10): 18-23.
[11] CHEN Hua-xi, XU Qing-bing. The fundamental theorem forAMHH in Yetter-Drinfeld module categories [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(8): 107-110.
[12] 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.
[13] WANG Yao, ZHOU Yun, REN Yan-li. Strongly 2-good Rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(2): 14-18.
[14] LU Qi, BAO Hong-wei. ZWGP-injectivity and nonsingularity of rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(2): 19-23.
[15] GAO Han-peng, YIN Xiao-bin. On strongly g(x)-J-clean rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(2): 24-29.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
[1] LIU Fang-yuan, MENG Xian-jia, TANG Zhan-yong, FANG Ding-yi, GONG Xiao-qing. Android application protection based on smali code obfuscation[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(3): 44 -50 .
[2] LIAO Xiang-wen, ZHANG Ling-ying, WEI Jing-jing, GUI Lin, CHENG Xue-qi, CHEN Guo-long. User influence analysis of social media with temporal characteristics[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(3): 1 -12 .
[3] GU Shen-ming, LU Jin-lu, WU Wei-zhi, ZHUANG Yu-bin. Local optimal granularity selections in generalized multi-scale decision systems[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(8): 1 -8 .
[4] ZHU Lin. Separated monic representations of quivers of type A4and RSS equivalences[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(2): 1 -8 .
[5] . Interval algorithm for mixed integer nonlinear two-level programming problems[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(2): 9 -17 .
[6] YAN Yan, HAO Xiao-hong. Differential privacy partitioning algorithm based on adaptive density grids[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(9): 12 -22 .
[7] CAO Wei-dong, DAI Tao, YU Jin-biao, WANG Xiao-hong, SHI An-feng. Improvement on the solution of pressure equation based on alternating direction in chemical flooding model[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(10): 88 -94 .
[8] LI Jin-hai, WU Wei-zhi. Granular computing approach for formal concept analysis and its research outlooks[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(7): 1 -12 .
[9] SUN Jian-dong, GU Xiu-sen, LI Yan, XU Wei-ran. Chinese entity relation extraction algorithms based on COAE2016 datasets[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(9): 7 -12 .
[10] SHAO Yong. Semilattice-ordered completely regular periodic semigroups[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(10): 1 -5 .
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd