Quotient rings and polynomial structures in the context of p-adic integers
Boubakeur Bahribahri.boubakeur@univ-khenchela.dzDepartment of MathematicsUniversity of Abbes LaghrourKhenchela, Algeria0000-0001-1311-0512View full profile → , Yassine Guerboussayassine_guer@hotmail.frDepartment of Computer ScienceKasdi Merbah UniversityOuargla, Algeria0000-0001-5518-0513View full profile → , Souad Ayadisouad.ayadi@univ-dbkm.dzDepartment of PhysicsFaculty of Materials Sciences and Computer ScienceAcoustics and Civil Engineering Laboratory, Thniet El Had StreetKhemis Miliana UniversityKhemis Miliana, 44225, Algeria0000-0001-7011-5389View full profile → , *Amina BoucennaCorresponding authorbenali4848@gmail.comDepartment of MathematicsFaculty of Exact Sciences and InformaticsLaboratory of Mathematics and Applications (LMA)Hassiba Benbouali UniversityChlef, 02000, Algeria0009-0006-9772-2799View full profile →
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- Received:
- 01 Nov 2025
- Published Online:
- 13 May 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-2686
- Pages:
- 2885–2895
Abstract
This work provides a comprehensive description of the quotient ring A/mn, where A = Z[ζ] and m = (1 – ζ) is a maximal ideal corresponding to a primitive p-th root of unity ζ. where [1] p is prime number . We explore the structure of A/mn for various values of n, highlighting its properties as a finite Artin local ring [2] and its connection to the p-adic integer ring Zp. By employing techniques from algebraic number theory, we explicitly describe the elements of A/mn, which facilitates the computation of sums and products of any two elements within this ring. This exposition not only elucidates the arithmetic structure of A/mn but also provides valuable insights into its relationship with cyclotomic fields and p-adic analysis [3].
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References
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