δ-Small submodule and Lifting property
DOI:
https://doi.org/10.29304/jqcm.2023.15.2.1243Keywords:
Singular submodule,, δ-small submodule,, δ-lifting module,, δ- hollow module,, S-L-hollow module.Abstract
In this paper, T is a commutative ring with identity. We were interested in providing A new conclusion about -small submodule by clarifying the connection between the lifting module and -small submodule. Moreover, by employing the concept -projective cover we illustrate how to put any submodule of the module as -small. In addition, we state the definition of -lifting module and associate it with additional concepts such as finitely generated and the property of cyclic module known as principally -lifting to get -small. Lastly, we explained the relationship between p- - hollow and -small in a certain conditions.
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References
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[10] Y. Ibrahim and M. Yousif,"Rad-Projective δ-Covers." Noncommutative Rings and Their Applications, vol.634, (2015), pp:175.
[11] Y. wang,"δ-small submodules, and δ-supplemented modules," International Journal of Mathematics and Mathematical Sciences, (2007).
[12] Z. Sharif and A. Alwan,"δ-Lifting and δ-Supplemented Semi modules," Journal of Optoelectronics Laser, vol.41, no.8, (2022), pp:164-171.
[2] A. F. Talak and M. M. Abed,"Duo submodule and C_1-module," Journal of Al-Qadisiya for computer science and mathematics, vol.13, no.1, (2021), pp:155-160.
[3] A. Hama and B. Al-Hashimi,"Hollow and Semihollow Modules," University of Sulaimani, College of Science, Department of Mathematics.
[4] F. Hameed,"On Local Modules Hollow Modules and Generalization," University Of Anbar-College of Education for Pure Sciences-Mathematics, (2021).
[5] F. W. Anderson and K. R. Fuller, Rings and categories of modules, New York: Springer Verlag, (1974).
[6] H. Inankil, S. Halicioglu , and A.Harmanci,"On a class of lifting modules," arXiv preprint arXiv:1312.4023, (2013).
[7] M. Abbas and M. Hamid,"A Note on Singular and Nonsingular Modules Relative to Torsion Theories," Mathematical Theory and Modeling, vol.3,(2013), pp:11-15.
[8] R. beyranvand and F. moradi,"Small submodules with respect to an arbitrary submodule," Journal of Algebra and related topics, vol.3, no.2, (2015), pp:43-51.
[9] S. Safaeeyon and N. Soboorishirazi,"Essential submodules with respect to an arbitrary submodule," Journal of Mathematical Extension. Vol.7, no.3, (2013), pp:15-27.
[10] Y. Ibrahim and M. Yousif,"Rad-Projective δ-Covers." Noncommutative Rings and Their Applications, vol.634, (2015), pp:175.
[11] Y. wang,"δ-small submodules, and δ-supplemented modules," International Journal of Mathematics and Mathematical Sciences, (2007).
[12] Z. Sharif and A. Alwan,"δ-Lifting and δ-Supplemented Semi modules," Journal of Optoelectronics Laser, vol.41, no.8, (2022), pp:164-171.
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Published
2023-09-25
How to Cite
Salih, B. A., & Abed, M. M. (2023). δ-Small submodule and Lifting property. Journal of Al-Qadisiyah for Computer Science and Mathematics, 15(2), Math Page 1–7. https://doi.org/10.29304/jqcm.2023.15.2.1243
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Math Articles
