Original Research Article

Article volume = 2024 and issue = 1

Pages: 19–22

Article publication Date: December 03, 2023

You can download PDF file of the article here: Download

Visited 68 times and downloaded 34 times

A Characterization of Commutative Rings in which every Semi Co-Hopfian Module is Artinian

Mankagna Albert Diompy(a), Remy Diaga Diouf(b), and Ousseynou Bousso(c)

(a) albertdiompy@yahoo.fr

(b) remydiaga.diouf@ucad.edu.sn

(c) ousseynou1.bousso@ucad.edu.sn


Let R be an associative ring with unit 1 ̸= 0, we call an unital left R-module M semi co-Hopfian (resp semi Hopfian ) if any injective (resp. surjective) endomorphism of M has a direct summand image (resp kernel). Starting from that every artinian module is co-Hopfian and so semi co-Hopfian, we showad in this paper that the class of ring on which every semi co-Hopfian module is artinian coincide with the class of artinian principal ideal rings when the v.p is satisfied. Moreover, some properties of this class of rings are given.


Semi co-Hopfian, Artinian, Vanaja property, SCHA-ring

  • [1] F. W. Anderson and K.R. Fuller: Rings and categories of modules, Springer-Verlag, Berlin 1974. 2.4
  • [2] P. Aydogdy and A. C. Ozcan: Semi co–Hopfian and Semi Hopfian Modules, Hacettepe University Department of Mathematics 06800 Beytepe, Ankara, Turkey 1
  • [3] V. A. Hiremath: Hopfian rings and Hopfian modules, Indian J. Pure Appl.Math. 17(7), 895-900 (1986). 1
  • [4] F. C. Leary co-Hopfian Modules, arXiv:2201.09961 [math.AC] (or arXiv:2201.09961v1 [math.AC] for this version) https://doi.org/10.48550/arXiv.2201.09961 2.3
  • [5] M. Sangharé, Sur le I-anneaux, les S-anneaux et les F-anneaux, Thèse d’Etat, Université Cheikh Anta Diop de Dakar, 17 Dec. 1993. 2.7, 2.8, 3
  • [6] W. V. Vasconcelos, Injective Endomorphisms of Finitely Generated Modules, Proceedings of the American Mathematical Society, Vol. 25, No. 4 (Aug., 1970), pp. 900-901. 3.5
Cite this article as:
  • Mankagna Albert Diompy, Remy Diaga Diouf, and Ousseynou Bousso, A Characterization of Commutative Rings in which every Semi Co-Hopfian Module is Artinian, Communications in Combinatorics, Cryptography & Computer Science, 2024(1), PP.19–22, 2023
  • Export citation to BibTeX