JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (8): 43-47, 56.doi: 10.6040/j.issn.1671-9352.0.2022.472

Previous Articles     Next Articles

Gorenstein weak projective comodules over a coalgebra

Longjiao YANG(),Hailou YAO*()   

  1. Department of Mathematics, Faculty of Science, Beijing University of Technology, Beijing 100124, China
  • Received:2022-09-07 Online:2023-08-20 Published:2023-07-28
  • Contact: Hailou YAO E-mail:y_ljiao@163.com;yaohl@bjut.edu.cn

RichHTML

1

PDF (PC)

160

Abstract:

The Gorenstein weak projective comodules over a coalgebra are introduced and studied. The relationships between weak projectivity and Gorenstein weak projectivity are obtained by using the push-out diagram and the short exact sequence of the left C-comodules. Meanwhile, an equivalent characterization is also obtained that a comodule is a Gorenstein weak projective comodule. Finally, n-Gorenstein weak projective comodules are intruoduced and proved that every n-Gorenstein weak projective comodule is a Gorenstein weak projective comodule, and if M is an n-Gorenstein weak projective comodule with finite projective dimension, then M is a weak projective comodule.

Key words: Gorenstein weak projective comodule, Gorenstein weak projective dimension, n-Gorenstein weak projective comodule

CLC Number: 

  • O153.3
1 BERTHELOT P , GROTHENDIECK A , ILLUSIE L . Théorie des intersections et théorème de Riemann-Roch[M]. Berlin: Springer, 1971.
2 GAO Z H , WANG F G . Weak injective and weak flat modules[J]. Communications in Algebra, 2015, 43 (9): 3857- 3868.
3 ZHAO T W , XU Y G . Remarks on Gorenstein weak injective and weak flat modules[J]. Algebra Colloquium, 2020, 27 (4): 687- 702.
doi: 10.1142/S1005386720000577
4 杨燕妮. n-Gorenstein弱内射模[J]. 数学的实践与认识, 2020, 50 (14): 200- 206.
YANG Yanni . On n-Gorenstein weak injective modules[J]. Mathematics in Practice and Theory, 2020, 50 (14): 200- 206.
5 BIERI R . Homological dimension of discrete groups[M]. London: Mathematics Department, Queen Mary College, 1976.
6 LIN B I-P . Semiperfect coalgebras[J]. Journal of Algebra, 1977, 49 (2): 357- 373.
doi: 10.1016/0021-8693(77)90246-0
7 郑跃飞. Gorenstein弱内射模[J]. 西南大学学报(自然科学版), 2011, 33 (12): 89- 92.
ZHENG Yuefei . Gorenstein weak-injective modules[J]. Journal of Southwest University (Natural Science Edition), 2011, 33 (12): 89- 92.
8 NASTASESCU C , TORRECILLAS B , ZHANG Y H . Hereditary coalgebras[J]. Communications in Algebra, 1996, 24 (4): 1521- 1528.
doi: 10.1080/00927879608825649
9 周伯壎. 同调代数[M]. 北京: 科学出版社, 1988.
ZHOU Boxun . Homology algebra[M]. Beijing: Science Press, 1988.
[1] 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.
[2] 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.
[3] Mengge GUAN,Hainan ZHOU,Junchao WEI. Some equivalent characterizations on EP elements [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(8): 13-17.
[4] Yao WANG,Jianghuan CHEN,Yanli REN. Quasi-J-clean rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(6): 1-8.
[5] YIN Jun-qi, YANG Gang. Gorenstein DG-injective complexes [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(10): 28-33.
[6] GUO Hui-ying, ZHANG Cui-ping. Ext-strong Ding projective modules [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(10): 31-36.
[7] 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.
[8] ZHAO Yang, ZHANG Wen-hui. Strongly Ding projective and strongly Ding injective modules over formal triangular matrix rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(10): 37-45.
[9] ZHAO Tiao, ZHANG Chao. q-Cartan matrices of self-injective Nakayama algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(10): 46-51.
[10] WANG Zhan-ping, YUAN Kai-ying. Strongly Gorenstein injective modules with respect to a cotorsion pair [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(8): 102-107.
[11] WU Xiao-ying, WANG Fang-gui. Graded version of Enochs theorem [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(10): 22-26.
[12] 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.
[13] ZHU Lin. Separated monic representations of quivers of type A4and RSS equivalences [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(2): 1-8.
[14] LI Jin-lan, LIANG Chun-li. Strongly Gorenstein C-flat modules [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(12): 25-31.
[15] 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.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
[1] LUO Si-te, LU Li-qian, CUI Ruo-fei, ZHOU Wei-wei, LI Zeng-yong*. Monte-Carlo simulation of photons transmission at alcohol wavelength in  skin tissue and design of fiber optic probe[J]. J4, 2013, 48(1): 46 -50 .
[2] TIAN Xue-gang, WANG Shao-ying. Solutions to the operator equation AXB=C[J]. J4, 2010, 45(6): 74 -80 .
[3] HUO Yu-hong, JI Quan-bao. Synchronization analysis of oscillatory activities in a biological cell system[J]. J4, 2010, 45(6): 105 -110 .
[4] TANG Feng-qin1, BAI Jian-ming2. The precise large deviations for a risk model with extended negatively upper orthant dependent claim  sizes[J]. J4, 2013, 48(1): 100 -106 .
[5] CHENG Zhi1,2, SUN Cui-fang2, WANG Ning1, DU Xian-neng1. On the fibre product of Zn and its property[J]. J4, 2013, 48(2): 15 -19 .
[6] TANG Xiao-hong1, HU Wen-xiao2*, WEI Yan-feng2, JIANG Xi-long2, ZHANG Jing-ying2, SHAO Xue-dong3. Screening and biological characteristics studies of wide wine-making yeasts[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(03): 12 -17 .
[7] ZHAO Jun1, ZHAO Jing2, FAN Ting-jun1*, YUAN Wen-peng1,3, ZHANG Zheng1, CONG Ri-shan1. Purification and anti-tumor activity examination of water-soluble asterosaponin from Asterias rollestoni Bell[J]. J4, 2013, 48(1): 30 -35 .
[8] YANG Yong-wei1, 2, HE Peng-fei2, LI Yi-jun2,3. On strict filters of BL-algebras#br#[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(03): 63 -67 .
[9] LI Min1,2, LI Qi-qiang1. Observer-based sliding mode control of uncertain singular time-delay systems#br#[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(03): 37 -42 .
[10] MAO Ai-qin1,2, YANG Ming-jun2, 3, YU Hai-yun2, ZHANG Pin1, PAN Ren-ming1*. Study on thermal decomposition mechanism of  pentafluoroethane fire extinguishing agent[J]. J4, 2013, 48(1): 51 -55 .
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd