Direct Sums of Prime Subsemimodules

Authors

  • Andi Muhammad Anwar Universitas Hasanuddin
  • Hanni Garminia INSTITUT TEKNOLOGI BANDUNG
  • Irawati Irawati INSTITUT TEKNOLOGI BANDUNG

DOI:

https://doi.org/10.20956/j.v18i2.16669

Keywords:

prime subsemimodules, fully prime semimodules, semirings

Abstract

Let  be a commutative semiring. A semimodule  over a semiring  is  a fully prime semimodule if each proper subsemimodule of  is prime. This research aims to investigate the relationship between a direct sum of prime subsemimodules   and  ,  , and a fully prime semimodule.

References

Anwar, A. M., Garminia, H. & Irawati, 2018. On the prime subsemimodules of multiplication semimodules. Far East Journal of Mathematical Sciences, 106(1), 151–157.

Dubey, M. & Sarohe, P., 2015. Generalizations of prime subsemimodules. Southeast Asian Bulletin of Mathematics, 39, 469-476.

Han, S.-C, 2017. Maximal and prime k-subsemimodules in semimodules over semirings. Journal of Algebra and Its Applications, 16, 1750130, 11pp.

M. Takahashi, 1981. On the bordism categories II: Elementary properties of semimodules. Math. Seminar Notes Kobe Univ, 9(2), 495-530

Shabir, M. & Iqbal, M.,2007. One-sided Prime Ideals in Semirings. Kyungpook Mathematical Journal, 47, 473–480.

Vandiver, H. S., 1934. Note on a simple type of algebra in which cancellation law of addition does not hold. Bull. Amer. Math. Soc, 40, 914-920..

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Published

2022-01-01

How to Cite

Anwar, A. M., Garminia, H. ., & Irawati, I. (2022). Direct Sums of Prime Subsemimodules. Jurnal Matematika, Statistika Dan Komputasi, 18(2), 169–173. https://doi.org/10.20956/j.v18i2.16669

Issue

Vol. 18 No. 2 (2022): JANUARY 2022

Section

Research Articles

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This work is licensed under a Creative Commons Attribution 4.0 International License.

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

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