DOI QR코드

DOI QR Code

SEMISIMPLE INJECTIVE COMODULE

  • AMR AMIN (Umm Al-Qura University, University college, Department of Mathematics) ;
  • NASR ZEYADA (Department of Mathematics, College of Science, University of Jeddah)
  • Received : 2022.11.05
  • Accepted : 2023.03.21
  • Published : 2023.07.30

Abstract

In this paper, we define the concept of a semisimple injective comodule. We show that it is a generalization of some known comodules, and we give a useful characterization of this notion. Finally, we obtain a new characterization of simple semiartinian coring using semisimple injective comodules.

Keywords

Acknowledgement

The author would like to thank the Deanship of Scientific Research at Umm Al-Qura University for supporting this work by Grant Code: (43405002).

References

  1. I. Amin, M. Yousif, N. Zeyada, Soc-injective rings and modules, Communication in Algebra 33 (2005), 4229-4250. https://doi.org/10.1080/00927870500279001
  2. F.W. Anderson, K.R. Fuller, Rings and Categories of Modules, Springer-Verlag, Berlin, 1974.
  3. T. Brzezinski and R. Wisbauer, Corings and Comodules, London Math. Soc. Lecture Note Series 309, Cambridge University Press, 2003.
  4. Lihong Dong, Shuan Xue, Xiaohui Zhang, The Factorization for a Class of Hom-Coalgebras, Advances in Mathematical Physics 2017 (2017), 14 pages. Article ID 4653172
  5. J. Gomez-Torrecillas, Separable functors in corings, International Journal of Mathematics and Mathematical Sciences 30 (2002), 23 pages. Article ID 627071
  6. Hans-E. Porst, On Corings and Comodules, Archivum Mathematicum 42 (2006), 419-425.
  7. FU Xue-rong and YAO Hai-lou, Indecomposable Injective Comodules Over Morita-Takeuchi Context Coalgebras, Journal of Beijing University of Technology 41 (2015), 1430-1436.
  8. R. Wisbauer, Semiperfect coalgebras over rings, in Algebras and Combinatorics, ICA97, Hong Kong, inequality problems, J. Appl. Math. and Computing 8 (2002), 123-245.