TARU PUBLICATIONS
Journal of Discrete Mathematical Sciences and Cryptography cover
Open Access ·Peer-reviewed·ISSN (Online): 2169-0065·ISSN (Print): 0972-0529

Monthly Journal: Publishes theoretical and applied research in all areas of Discrete Mathematical Sciences, Cryptography, Combinatorics, Elliptic Curves and Information Security.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
submissions@tarupublications.com
Open Access Research Article

Small subsemimodule and some related concepts

* ,

* Corresponding author · click or hover a name for details

pp. 617–623Vol. 28Issue 2March 2025DOI: 10.47974/JDMSC-2280 Crossmark XML
Received:
13 Nov 2024
Published Online:
11 Apr 2025
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-2280
Pages:
617–623

Abstract

Previously, some authors have studied the concept of small submodules regarding semirings. This research aims to provide a comprehensive study of small modules and some related concepts as: cosemisimple semiring, semimodule with finite spanning dimension, small free semimodule and small projective semimodule. These concepts are implemented and studied in various modules. Then we convert it to semimodule and give some results.

Keywords

Subject Classifications

26A1828Dxx

References

[1] N.X. Tuyen and H.X. Thang, On Superfluous Subsemimodules, gmj, vol. 10, no. 4, pp. 763-770 (2003). [Online] Available: https://doi.org/10.1515/gmj.2003.763.
[2] R. Wisbauer, Foundations of Modules and Rings Theory, Gordan and Breach Reading (1991).
[3] A.M. Alhossaini, and Z.A. Aljebory, Fully Dual Stable Semimodule. Journal of Iraqi Al-khwarizmi, Vol. 1, no. 1, pp. 92-100 (2017).
[4] M.M. Altaee, and A.A. Alhossaini, π-Projective Semimodule Over Semiring. Journal of University of Babylon for Pure and Applied Sciences, Vol. 28, no. 1, pp. 121-137.  (2020). 
[5] J. Abuhlail, Exact sequences of semimodules over semirings. arXiv preprint (2012). [Online] Available: https://arxiv.org/abs/1210.4566 
[6] K.R. Fuller, and F.W. Anderson, Rings and categories of modules. Springer-Verlage (1992).
[7] P. Fleury, Hollow modules and local endomorphism rings, Pac. J. Math., vol. 53, no. 2, pp. 379-385 (1974). [Online] Available: https://doi.org/10.2140/pjm.1974.53.379.
[8] J.S. Golan, Semirings and their Applications. Springer Science and Business Media. (2013).
[9] K.M. Rangaswamy, “Modules with Finite Spanning Dimension,” Can. Math. Bull., vol. 20, no. 2, pp. 255-262 (1977). [Online] Available: https://doi.org/10.4153/cmb-1977-039-4.
[10] A.K. Tiwary, and K.N. Chaubey, Small Projective Module. Indian J. Pure Appl, vol. 16, no. 2, pp. 133-138 (1985).
[11] S.Alhashemi, and A.M. Alhossaini, Extending Semimodule and Singularity. The seventh scientific conference of the Al-Khwarizmi society, in cooperation with the technical institute-Mosul, pp.330-340 (2021).
[12] H.M.J. Al-Thani, Projective and Injective Semimodules over Semirings, Doctoral dissertation, University of East London (1998).
[13] M. Takahashi, On the bordism categories II. In Mathematics seminar notes. Vol. 9, No. 2, pp. 495-530 (1981).
[14] R.A. Shaban, E.Y. Abdullah, and A.N. Albukhuttar, “Study unsteady flow of synovial fluid in the elastic porosity of layers using double ZZ transformation,” J. Interdiscip. Math., vol. 25, no. 6, pp. 1933-1950 (2022). [Online] Available: https://doi.org/10.1080/09720502.2022.2093438.
[15] S.A. Mehdi, E.A. Kuffi, and J A. Jasim, “Solving ordinary differential equations using a new general complex integral transform,” J. Interdiscip. Math., vol. 25, no. 6, pp. 1919-1932 (2022). [Online] Available: https://doi.org/10.1080/09720502.2022.2089381.
[16] E.A. Mansour, E.A. Kuffi, and S.A. Mehdi, “Applying SEE transform in solving Faltung type Volterra integro-differential equation of first kind,” J. Interdiscip. Math., vol. 25, no. 5, pp. 1315-1322 (2022). [Online] Available: https://doi.org/10.1080/09720502.2022.2040848.
[17] S.M. Kadham and M.A. Mustafa, “Medical applications of the new-transform,” J. Interdiscip. Math., vol. 26, no. 6, pp. 1341-1353 (2023). [Online] Available: https://doi.org/10.47974/jim-1632.
[18] S.M. Kadham and M.A. Mustafa, “Fuzzy SHmath.Mbio-transform generalization and application to skin cancer imaging (distributed diseases),” J. Interdiscip. Math., vol. 26, no. 6, pp. 1031-1042 (2023). [Online] Available: https://doi.org/10.47974/jim-1603.

Views: 231Downloads: 116Citations: 0