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

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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

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.
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