On distributive semimodules
DOI:
https://doi.org/10.31642/JoKMC/2018/100209%20Keywords:
distributive semimodule, subtractive, semisubtractive, k-cyclic,, weak distributive.Abstract
This work considers the construction of the concept of distributive property for semimodules. Some characterizations of this property, with some examples are given. Some conditions on semiring or semimodules (like subtractive, semisubtractive, cancellative, and k-cyclic) are required to obtain interesting results. The main results are: Any subsemimodule and factor semimodule of a distributive semimodule is distributive. Moreover, weakly distributive, is also, introduced and investigated. It is found that the semimodule is distributive if and only if each subsemimodule is weak distributive. Taking advantage of the supplemented concept to find some properties of distributive semimodule. Finally, the summand sum and summand intersection properties for distributive semimodules with some conditions are valid.
Downloads
References
J. Saffar Ardabili, S. Motmaen and A. Yousefian Darani, "The Spectrum of Classical Prime Subsemimodules," Australian Journal of Basic and Applied Sciences, vol. 7, no. 11, pp. 1824-1830, 2011.
Zaidoon W. Alboshindi and Asaad A.M. Alhossaini, "Fully Prime Semimodule, Fully Essential Semimodule and Semi-Complement Subsemimodules," Iraqi Journal of Science, vol. 63, no. 12, pp. 5455-5466, 2022.
W. Stphenson, "Modules whose lattice of submodules is distributive," Proc. London Math Soc, pp. 291-310, 28 1974.
V. Camillo, "Distributive modules," J.Algebra, no. 36, pp. 16-25, 1975.
V. Erdoğdu, "Distributive modules," Canad. Math. Bull, vol. 30(2), pp. 248-254, 1987.
A. V. Mikhalev and A. A. Tuganbaev, "Distributive modules and rings and their close analogs," Journal of Mathematical Sciences, vol. 93(2), pp. 149-253, 1999.
J. S. Golan, Semirings and Their Applications, Kluwer Academic Publishers, Dordrecht, 1999.
A. H. Alwan, "Maximal ideal graph of commutative semirings," International Journal of Nonlinear Analysis and Applications, vol. 12, no. 1, pp. 913-926, 2021.
M.T.Altaee and A .M. A. Alhossanini, "Π-Injective Semimodule over Semiring," Solid State Technolog, vol. 63, no. 5, pp. 3424-3433, 2020.
Vishnu Gupta and J.N. Chaudhari , "Some remarks on semirings," Radovi Matematicki, vol. 12, pp. 13–18, 2003.
Tuyen, Nguyen Xuan, and Ho Xuan Thang, "On superfluous subsemimodules," Georgian Mathematical Journal, vol. 10, no. 4, pp. 763-770, 2003.
Ali H. A. Alhamti and Asaad M. A. Alhossaini, "The homomorphisms of distributive semimodules". To appear, Iraqi Journal of Science.
E. D. Sow, "On Essential Subsemimodules and Weakly Co-Hopfion," European Journal of pur and applied Mathematics, Vol. 9, No. 3, pp. 250-265, 2016.
J. R. Tsiba and D. Sow, "On Generators and Projective Semimodules," International Journal of Algebra, vol. 4, no. 24, pp. 1153-1167, 2010.
Muna M. T. Altaee and Asaad M. A. Alhossaini, "Supplemented and π-Projective Semimodules," raqi Journal of Science, pp. 1479-1487, 2020.
Khitam S. H. Aljebory and Assad M. A. Alhossaini, "Principally Quasi-Injective Semimodules," Baghdad Science Journal, vol. 16, no. 4, pp. 28-936, 2019.
R. E. Atani, and Sh. E. Atani, "On subsemimodules of semimodules," Buletinul Academiei de Ştiinţe a Moldovei. Matematica, vol. 2, no. 63, pp. 20-30, 2010.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 Ali Hasan abdulkhaliq, Asaad Alhossaini
This work is licensed under a Creative Commons Attribution 4.0 International License.
which allows users to copy, create extracts, abstracts, and new works from the Article, alter and revise the Article, and make commercial use of the Article (including reuse and/or resale of the Article by commercial entities), provided the user gives appropriate credit (with a link to the formal publication through the relevant DOI), provides a link to the license, indicates if changes were made and the licensor is not represented as endorsing the use made of the work.
