Original Research Article

Article volume = 2023 and issue = 2

Pages: 132–139

Article publication Date: November 25, 2023

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Principally Supplemented Semimodules

Ahmed H. Alwan

Department of Mathematics, College of Education for Pure Sciences, University of Thi-Qar, Thi-Qar, Iraq

Abstract:

In this work, principally supplemented semimodules are defined which generalize supplemented semimodules. Some properties of principally supplemented semimodules are investigated. We show that if A = A1 ⊕A2 is duo semimodule with A1 and A2 are principally supplemented semimodules, then A is principally supplemented. It is also proved that if A is an indecomposable semimodule, then A is principally supplemented semimodule if and only if A is principally lifting semimodule.

Keywords:

Supplemented semimodules, Lifting semimodules, Principally supplemented semimodules, Principally lifting semimodules, Semiperfect semimodules.

References:
  • [1] F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, Springer-Verlag, New York, (1974). 3
  • [2] U. Acar and A. Harmanci, Principally Supplemented Modules, Albanian J. Math., 4(3), (2010), 74-78. 3, 3.7, 3, 4
  • [3] A. H. Alwan and A. M. Alhossaini, On dense subsemimodules and prime semimodules, Iraqi Journal of Science, 61(6), (2020), 1446-1455. 1
  • [4] A. H. Alwan and A. M. Alhossaini, Dedekind multiplication semimodules, Iraqi Journal of Science, 61(6), (2020), 1488-1497. 1
  • [5] A. H. Alwan, Small intersection graph of subsemimodules of a semimodule, 7th International Conference on Combinatorics, Cryptography, Computer Science and Computing, November 16-17, (2022). 1, 2
  • [6] A. H. Alwan, Ss-supplemented semimodules, Journal of Interdisciplinary Mathematics , 26(5), (2023), 881-888. 1
  • [7] A. H. Alwan, Generalizations of supplemented and lifting semimodules, Iraqi Journal of Science to appear (2024). 1, 2.3, 3.11, 3.15, 3.20, 3.22, 3.23, 4.4, 4.5
  • [8] J. S. Golan, semirings and their applications, Kluwer Academic Publishers, Dordrecht, (1999). 1, 4
  • [9] H. Sh. Khareeba, A. H. Alwan, Generalized supplemented semimodules, Journal of Electronics, Computer Networking and Applied Mathematics, 3(5), (2023), 28-35.
  • [10] H. Sh. Khareeba, A. H. Alwan, Cofinitely lifting semimodules, Eurasian Journal of Physics, Chemistry and Mathematics, vol. 20, (2023), 1-7. 1
  • [11] Z. R. Sharif and A. H. Alwan, δ -Lifting and δ-Supplemented Semimodules, Journal of Optoelectronics Laser, 41(8), (2022), 164-171. 1
  • [12] Z. R. Sharif and A. H. Alwan, δ -Semiperfect Semirings and δ-Lifting Semimodules, Journal of Optoelectronics Laser, 41(8), (2022), 172-177. 4.3
  • [13] N. X. Tuyen and H. X. Thang, On superfluous subsemimodules, Georgian Math J., 10(4), (2003), 763-770. 1, 2, 4.1, 4.2
  • [14] R. Wisbauer, Foundations of module and ring theory, Gordon and Breach, (1991). 1
Cite this article as:
  • Ahmed H. Alwan, Principally Supplemented Semimodules, Communications in Combinatorics, Cryptography & Computer Science, 2023(2), PP.132–139, 2023
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