Multiplication Module and Retractable Concept
DOI:
https://doi.org/10.29304/jqcm.2023.15.2.1245Keywords:
Multiplication module, Retractable module,, Division module, Injective module,, Simple module.Abstract
In this paper; we study a strong relation between faithful multiplication module and retractable concept. We proved that if M is faithful and cyclic, so is retractable. On the other hand, faithful injective Module with multiplication property gives retractable module. Also, finitely generated semi-simple module over quasi-invariant ring is retractable module. Finally, some definitions, examples and properties have been presented about retractable module.
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References
[1] I. Mohammed Ali Hadi and Sh. Neamah, Studying Some Results about Completely Coretractable Ring (CC-ring), Global Journal of Mathematics, Vol. 10, No. 1, 2017.
[2] Z. Julius. (1981). Weakly primitive rings. Communications in Algebra. 9. 23-45. 10.1080/00927878108822561.
[3] F. Hammad & M. Abed (2021). A New Results of Injective Module with Divisible Property. Journal of Physics: Conference Series. 1818. 012168. 10.1088/1742-6596/1818/1/012168.
[4] A. Wardayani, I. Kharismawati, I. Sihwaningrum, (2020). Regular rings and their properties. Journal of Physics: Conference Series. 1494. 012020. 10.1088/1742-6596/1494/1/012020
[5] V. Erdoğdu (1987). Distributive Modules. Canadian Mathematical Bulletin, 30(2), 248–254. https://doi.org/10.4153/cmb-1987-035-x
[6] E. Atani, Shahabaddin & S. Ghaleh.. (2006). On multiplication modules. International Mathematical Forum.
[7] R. Rajaa , Sh. Pirzada. (2020). Essential ideals represented by mod-annihilators of modules. Arxiv, 2203.02463vl.
[8] Sh. Al-aeashi & B. Davvaz. (2021). On Fully Closed Stable Modules. Walailak Journal of Science and Technology (WJST). 18. 10.48048/wjst.2021.9534.
[9] P. F. Smith. (2012). On injective and divisible modules, Arabian Journal of Mathematics, 1:127–137(10.1007/s40065-012-0011–8).
[10] M. Mohammed Abed, F.Al-Sharqi and S. H. Zail, Injective Modules, Projective Modules and Their Relationship to Some Rings, AIP Coference Proceeding 2472, 030002 (2022).
[11] I. M. A. Hadi, & S. N. Al-Aeashi, (2017). P-Coretractable and Strongly P-Coretractable Modules. Asian Journal of Applied Sciences. https://doi.org/10.24203/ajas.v5i2.4714
[12] Faith, C.C. (1967). Lectures on injective modules and quotient rings. Volume 49, springer-verlag, Benin Heidelberg, Newyork.
[2] Z. Julius. (1981). Weakly primitive rings. Communications in Algebra. 9. 23-45. 10.1080/00927878108822561.
[3] F. Hammad & M. Abed (2021). A New Results of Injective Module with Divisible Property. Journal of Physics: Conference Series. 1818. 012168. 10.1088/1742-6596/1818/1/012168.
[4] A. Wardayani, I. Kharismawati, I. Sihwaningrum, (2020). Regular rings and their properties. Journal of Physics: Conference Series. 1494. 012020. 10.1088/1742-6596/1494/1/012020
[5] V. Erdoğdu (1987). Distributive Modules. Canadian Mathematical Bulletin, 30(2), 248–254. https://doi.org/10.4153/cmb-1987-035-x
[6] E. Atani, Shahabaddin & S. Ghaleh.. (2006). On multiplication modules. International Mathematical Forum.
[7] R. Rajaa , Sh. Pirzada. (2020). Essential ideals represented by mod-annihilators of modules. Arxiv, 2203.02463vl.
[8] Sh. Al-aeashi & B. Davvaz. (2021). On Fully Closed Stable Modules. Walailak Journal of Science and Technology (WJST). 18. 10.48048/wjst.2021.9534.
[9] P. F. Smith. (2012). On injective and divisible modules, Arabian Journal of Mathematics, 1:127–137(10.1007/s40065-012-0011–8).
[10] M. Mohammed Abed, F.Al-Sharqi and S. H. Zail, Injective Modules, Projective Modules and Their Relationship to Some Rings, AIP Coference Proceeding 2472, 030002 (2022).
[11] I. M. A. Hadi, & S. N. Al-Aeashi, (2017). P-Coretractable and Strongly P-Coretractable Modules. Asian Journal of Applied Sciences. https://doi.org/10.24203/ajas.v5i2.4714
[12] Faith, C.C. (1967). Lectures on injective modules and quotient rings. Volume 49, springer-verlag, Benin Heidelberg, Newyork.
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Published
2023-09-25
How to Cite
Jumaa, H. A., & Abed, M. M. (2023). Multiplication Module and Retractable Concept. Journal of Al-Qadisiyah for Computer Science and Mathematics, 15(2), Math Page 14–21. https://doi.org/10.29304/jqcm.2023.15.2.1245
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Math Articles
