The Characterization of Almost Prime Submodule on the Finitely Generated Module over Principal Ideal Domain

Wardhana, I Gede Adhitya Wisnu
Astuti, Pudji
Muchtadi-Alamsyah, Intan

Journal of the Indonesian Mathematical Society
VOLUME 30 NUMBER 1 (MARCH 2024)

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.