Semi-complement Co-Hopfian R-mods

Abdullah, Nada Khalid

doi:10.47974/JIM-1574

Open Access Research Article

Semi-complement Co-Hopfian R-mods

^*Nada Khalid AbdullahCorresponding authornada.khalid@tu.edu.iqDepartment of MathematicsCollege of Education for Pure ScienceTikrit UniversityTikrit, IraqView full profile →

* Corresponding author · click or hover a name for details

pp. 625–633Vol. 27Issue 4June 2024DOI: 10.47974/JIM-1574XML

Received:: 23 Oct 2023
Published Online:: 31 May 2024
Article type:: Research Article
Language:: EN
Article no.:: JIM-1574
Pages:: 625–633

Abstract

This study presents a semi-complement Co-Hopfian R-module (si-Cp Co-Hop. mod). The proposal is a monomorphic endomorphism of X with a si-comp image, which is a generalization of the Co-Hop. Mod. This article introduces some properties of the si-Cp Co-Hop, mod, and an investigation with examples. Furthermore, the current study deals with this class of mods and gives several fundamental properties related to this concept.

Keywords

Semi-complement submod Co-Hopfian module Semi-complement co-Hopfian module

Subject Classifications

11J9311G09

References

[1] Alatuany, Aseel Amer Hassan. Essential-small fully stable modules. International Journal of Nonlinear Analysis and Applications, 12.2: 1811-1816 (2021).
[2] Asgari, Sh; Haghany, A. Densely co-Hopfian modules. Journal of Algebra and Its Applications, 9.06 : 989-1000 (2010).
[3] Asgari, Sh. On weakly co-Hopfian modules (2007).
[4] Asgari, Sh; Haghany, A.; Vedadi, M. R. Quasi co-Hopfian modules and applications. Communications in Algebra®, 36.5: 1801-1816 (2008).
[5] Gdu, Pınar Aydo; Ozcan, A. Cigdem. Semi co–Hopfian and Semi Hopfian Modules.
[6] Breaz, Simion; Calugareanu, Grigore; Schultz, Phill. Modules with Dedekind finite endomorphism rings. Mathematica, 53.76 : 15-28 (2011).
[7] Dung, Nguyen Viet. Extending modules. Routledge (2019).
[8] Goodearl, Kenneth. Ring theory: Nonsingular rings and modules. CRC Press (1976).
[9] HADI, Inaam Mohammed Ali; SHYAA, Farhan Dakhil. T-Stable-extending Modules and Strongly T-stable Extending Modules. Iraqi Journal of Science, 401-408 (2020).
[10] Haghany, A.; Vedadi, M. R. Modules whose injective endomorphisms are essential. Journal of Algebra, 243.2: 765-779 (2001).
[11] Hamid, Sufyan A.; Abdullah, Nada K. Complement Hopfian Module. Tikrit Journal of Pure Science, 25.3: 121-123 (2020).
[12] Divaani-Aazar, Kamran; Mafi, Amir. Hopfian and co-Hopfian modules over commutative rings. Vietnam J. Math, 35.3: 275-283 (2007).
[13] Khalaf Yahya Hatam. Maximal and semi maximal, Ph.D. Thesis, University of Baghdad, College of Education, Ibn-Al-Haitham (2007).
[14] Rasha Naser Majeed. ON Min(Max)-CS Modules, M.Sc. Thesis, college of Education, Ibn Al-Haitham, University of Baghdad (2011).
[15] Özcan, A. C.; Harmanci, Ayla; Smith, P. F. Duo modules. Glasgow Mathematical Journal, 48.3 : 533-545 (2006).
[16] Salman, Z. T. Purely co-Hopfian Modules. Ibn AL-Haitham Journal For Pure and Applied Science, 25.2 (2017).
[17] Maurya, S. K., & Gupta, A. J. A note on direct-injective modules. Palestine Journal of Mathematics, 8(1) (2019).
[18] Rad, P. M., & Mahdavi, L. A. A note on the intersection graph of submodules of a module. Journal of Interdisciplinary Mathematics, 22(4), 493-502 (2019).
[19] Salih, M. A., Majeed, T. H., & Nayef, M. S. On duality of injective topological module. Journal of Interdisciplinary Mathematics, 25(5), 1409-1414 (2022).

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