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Date Published: 30/05/2025
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DOI: https://doi.org/10.54607/hcmue.js.22.5.4730(2025)
Issue
Vol. 22 No. 5 (2025)
Section
Articles
How to Cite
Cao, P. A. D., & My, V. Q. (2025). THE STRUCTURE OF MULTIPLICATIVE GROUPS OF RESIDUE CLASS RINGS OF THE EISENSTEIN INTEGERS. HCMUE Journal of Science, 22(5), 814-823. https://doi.org/10.54607/hcmue.js.22.5.4730(2025)

THE STRUCTURE OF MULTIPLICATIVE GROUPS OF RESIDUE CLASS RINGS OF THE EISENSTEIN INTEGERS

Cao Phan Anh Dung1, My Vinh Quang1,
1 Trường Đại học Sư phạm Thành phố Hồ Chí Minh

Main Article Content

Abstract

This paper presents a comprehensive analysis of residue class ring of the Eisenstein integer ring modulo powers of prime elements. As a consequence, we also characterize the structure of the multiplicative group modulo arbitrary (composite) Eisenstein integers. Additionally, we determine all Eisenstein integers that admit primitive roots. 

Keywords

Eisenstein integers, multiplicative groups, primitive roots

Article Details

References

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