A Note on Free Module Decomposition over A Principal Ideal Domain

Ni Wayan Switrayni; I Gede Adhitya Wisnu Wisnu Wardhana; Qurratul Aini

doi:10.22342/jims.29.2.1246.150-155

Ni Wayan Switrayni ⁽¹⁾ , I Gede Adhitya Wisnu Wisnu Wardhana ⁽²⁾ , Qurratul Aini ⁽³⁾

(1) Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Mataram, Indonesia,

(2) University of Mataram, Indonesia,

(3) Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Mataram, Indonesia

https://doi.org/10.22342/jims.29.2.1246.150-155

Issue
VOLUME 29 NUMBER 2 (JULY 2023)

Submitted
July 4, 2022

Accepted
April 13, 2023

Published
July 18, 2023

Keywords:

Endomorphism, Free Module, Principal Ideal Domain, Eigen Space

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Abstract

Some methods have been used to express a finitely generated module over a principal ideal domain as a finite direct sum of its cyclic submodules. In this paper, we give an alternative technique to decompose a free module with finite rank over a principal ideal domain using eigen spaces of its endomorphism ring.

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References

I. G. A. W.Wardhana, The Decomposition ofa Finitely Generated Module over Some Special Ring, Jurnal Teori dan Aplikasi Matematika 6(2) (2022), 261-267.

W. C. Brown, Matrices Over Commutative Rings, Marcel Dekker, Inc., New York, 1993. [3] S. Hadjirezaei, S. Hedayat, Decomposition ofFinitely Generated Modues Using Fitting Ideals, Czechoslovak Mathematical Journal 70 (2020), no.4 1179–1190.

X. R. Ma, H. G. Liu, H. L. Zhang, A Note on Finitely Generated Modules over a PID, Advances in Pure Mathematics 10(12) (2020), 699–705.

S. Roman, Advanced Linear Algebra, Third Edition, Springer Science+Business Media, LLC, New York, 2008.

Authors

Ni Wayan Switrayni

Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Mataram

I Gede Adhitya Wisnu Wisnu Wardhana

University of Mataram

adhitya.wardhana@unram.ac.id (Primary Contact)

Qurratul Aini

Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Mataram

Switrayni, N. W., Wardhana, I. G. A. W. W., & Aini, Q. (2023). A Note on Free Module Decomposition over A Principal Ideal Domain. Journal of the Indonesian Mathematical Society, 29(2), 150–155. https://doi.org/10.22342/jims.29.2.1246.150-155