Some characteristics of cyclic prime, weakly prime and almost prime submodule of Gaussian integer modulo over integer

Juliana, Rina; Wardhana, I Gede Adhitya Wisnu; Irwansyah,

doi:10.1063/5.0042586

Cited by 3 publications

(2 citation statements)

References 4 publications

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“…This study is based on the characterizations of cyclic prime submodule, and we generalize it into a more advanced module, a finitely generated module (Juliana et al, 2021). This research was using deductive proof based on a literature study in the form of books and scientific journals, especially those related to the module theory.…”

Section: B Methodsmentioning

confidence: 99%

The Decomposition of a Finitely Generated Module over Some Special Ring

Wardhana

2022

JTAM

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This research aims to give the decompositions of a finitely generated module over some special ring, such as the principal ideal domain and Dedekind domain. One of the main problems with module theory is to analyze the objects of the module. This research was using a literature study on finitely generated modules topics from scientific journals, especially those related to the module theory. And by selective cases we find a pattern to build a conjecture or a hypothesis, by deductive proof, we prove the conjecture and state it as a theorem. The main result in this study is the decomposition of the finitely generated module is a direct sum of the torsion submodule and torsion-free submodule. Since the torsion-free module is always a free module over a principal ideal domain, then the torsion-free submodule is a free module. Last, we generalize the ring, from a principal ideal domain, to a Dedekind domain. We found then the torsion-free submodule became a projective module. Then the decomposition of the finitely generated module is a direct sum of the torsion submodule and the projective submodule. These results should help the researchers to analyze the objects on module theory.

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Section: B Methodsmentioning

confidence: 99%

The Decomposition of a Finitely Generated Module over Some Special Ring

Wardhana

2022

JTAM

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“…However, these results were still limited to 2 × 2 -matrices and each cyclic submodule in the internal direct sum can still be decomposed into some smaller submodules. See [1] [6] for others module decomposition. Therefore, in this paper, we discuss a cyclic decomposition of module of matrices with entries over integer modulo n and arbitrary size (not only square matrices), M m×r (Z n ), which is considered as a module over ring Z using the primary decomposition theorem.…”

Section: Introductionmentioning

confidence: 99%

ON CYCLIC DECOMPOSITION OF Z-MODULE M_{m×r}(Z_n)

Switrayni,

Wardhana,

Aini

2022

JFMA

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A note on almost prime submodule of CSM module over principal ideal domain

Wardhana

Nghiem

Switrayni

et al. 2021

J. Phys.: Conf. Ser.

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An almost prime submodule is a generalization of prime submodule introduced in 2011 by Khashan. This algebraic structure was brought from an algebraic structure in ring theory, prime ideal, and almost prime ideal. This paper aims to construct similar properties of prime ideal and almost prime ideal from ring theory to module theory. The problem that we want to eliminate is the multiplication operation, which is missing in module theory. We use the definition of module annihilator to bridge the gap. This article gives some properties of the prime submodule and almost prime submodule of CMS module over a principal ideal domain. A CSM module is a module that every cyclic submodule. One of the results is that the idempotent submodule is an almost prime submodule.

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Some characteristics of cyclic prime, weakly prime and almost prime submodule of Gaussian integer modulo over integer

Cited by 3 publications

References 4 publications

The Decomposition of a Finitely Generated Module over Some Special Ring

The Decomposition of a Finitely Generated Module over Some Special Ring

ON CYCLIC DECOMPOSITION OF Z-MODULE M_{m×r}(Z_n)

A note on almost prime submodule of CSM module over principal ideal domain

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