Article Per Year (5 Year)
p-Index From 2020 - 2025
0.23
P-Index
This Author published in this journals
All Journal Indonesian Journal of Applied Mathematics and Statistics
Cahyadi, Arya Raditya
Unknown Affiliation
Computer Science & IT Decision Sciences, Operations Research & Management Education Engineering Public Health

Published : 1 Documents Claim Missing Document
Claim Missing Document
Check
Articles

Found 1 Documents
Search

 1 
Necessary and Sufficient Conditions for a Finite Cyclic Group to be a Cyclic Module Cahyadi, Arya Raditya; Sylviani, Sisilia; Gyenin, Mary
Indonesian Journal of Applied Mathematics and Statistics Vol. 2 No. 2 (2025): Indonesian Journal of Applied Mathematics and Statistics (IdJAMS)
Publisher : Lembaga Penelitian dan Pengembangan Matematika dan Statistika Terapan Indonesia, PT Anugrah Teknologi Kecerdasan Buatan PT Anugrah Teknologi Kecerdasan Buatan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.71385/idjams.v2i2.28

Abstract

The structures of cyclic groups and cyclic modules are fundamental topics in abstract algebra. While their individual structures are well-established, the precise conditions that link them over an arbitrary ring  are often not detailed in the literature. This paper aims to find the necessary and sufficient conditions for a finite cyclic group  of order n to be a cyclic -module for an arbitrary ring . The method used in this research is by utilizing the fundamental theorem stating a relationship between an abelian group viewed as a -module and a ring homomorphism from  to the ring of endomorphism of its group, which is isomorphic to . The result of this research is a theorem proving that a finite cyclic group  of order  can be endowed with the structure of a cyclic -module if and only if there exists a surjective ring homomorphism from  to  (the ring of integers modulo ). This finding establishes a clear connection between these algebraic structures.
Co-Authors Gyenin, Mary Sisilia Sylviani