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. 

Article Details

References

Alaca, S., & Williams, K. S. (2004). Introductory Algebraic Number Theory. Cambridge University Press.
Bolker, E. D. (1970). Elementary Number Theory. W. A. Benjamin.
Cross, J. T. (1983). The Euler φ-function in the Gauss integers. American Mathematical Monthly, 90(8), 518-528.
Titu, A., Andreescu, T., & Mushkarov, O. (2017). Number Theory: Concepts and Problems. XYZ Press.