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Abstract
In most cases, almost prime submodules are equivalent to prime submodules, but in a finitely generated module, it is not necessarily equivalent. Based on the fact that a finitely generated module over a principal ideal domain can be decomposed into a free part and a torsion part, we give a new approach to the characteristic of almost prime submodules in the finitely generated module, especially we point out the cases when the submodules are almost prime but not prime.
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References
- Kashan, H.A., ”On Almost Prime Submodules”, Acta Mathematica Scientia 32B(2) (2012), 29 645-651.
- Wardhana, I.G.A.W., Nghiem, N.D.H., Switrayni, N.W., Aini, Q. ”A note on almost prime submodule of CSM module over principal ideal domain”, Journal of Physics: Conference Series 2106(1) (2021), 012011.
- Wardhana, I.G.A.W., Astuti, P., Muchtadi-Alamsyah, I. ”On almost prime submodules of a module over a principal ideal domain”. JP Journal of Algebra, Number Theory and Applications, 38(1) (2016), 121-130.
- Wardhana, I.G.A.W. ”The Decomposition of a Finitely Generated Module over Some Special Ring” Jurnal Teori dan Aplikasi Matematika, 6(1) 2022, 261-267.
- Kaplansky I (2022). ”Infinite Abelian groups” Bull Oz, AW.
- Hedayat, S., Nekooei, R. ”Characterization of Prime Submodules of a Finitely Generated Free Module over a PID”, Houston Journal of Mathematics, 31(1), 75-85.
References
Kashan, H.A., ”On Almost Prime Submodules”, Acta Mathematica Scientia 32B(2) (2012), 29 645-651.
Wardhana, I.G.A.W., Nghiem, N.D.H., Switrayni, N.W., Aini, Q. ”A note on almost prime submodule of CSM module over principal ideal domain”, Journal of Physics: Conference Series 2106(1) (2021), 012011.
Wardhana, I.G.A.W., Astuti, P., Muchtadi-Alamsyah, I. ”On almost prime submodules of a module over a principal ideal domain”. JP Journal of Algebra, Number Theory and Applications, 38(1) (2016), 121-130.
Wardhana, I.G.A.W. ”The Decomposition of a Finitely Generated Module over Some Special Ring” Jurnal Teori dan Aplikasi Matematika, 6(1) 2022, 261-267.
Kaplansky I (2022). ”Infinite Abelian groups” Bull Oz, AW.
Hedayat, S., Nekooei, R. ”Characterization of Prime Submodules of a Finitely Generated Free Module over a PID”, Houston Journal of Mathematics, 31(1), 75-85.