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..

Downloads

Published

2022-01-01

Issue

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

Section

Research Articles

License

Copyright (c) 2021 Author and publisher

Creative Commons License

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.

Jurnal Matematika, Statistika dan Komputasi is an Open Access journal, all articles are distributed under the terms of the Creative Commons Attribution License, allowing third parties to copy and redistribute the material in any medium or format, transform, and build upon the material, provided the original work is properly cited and states its license.  This license allows authors and readers to use all articles, data sets, graphics and appendices in data mining applications, search engines, web sites, blogs and other platforms by providing appropriate reference.


Deprecated: json_decode(): Passing null to parameter #1 ($json) of type string is deprecated in /home/journal33/public_html/plugins/generic/citations/CitationsPlugin.inc.php on line 49