Cyclotomy, cyclotomic cosets and arithmetic properties of some families in $ \frac{\mathbb{F}_l[x]}{\langle x^{p^sq^t}-1\rangle} $
Abstract
Arithmetic properties of some families in $ \mathbb{F}_l[x]/\langle x^{p^sq^t}-1\rangle $ were obtained by using the cyclotomic classes of order 2 with respect to $ n = p^sq^t $, where $ p\equiv3\ \mathrm{mod}\ 4 $, $ \gcd(\phi(p^s), \phi(q^t)) = 2 $, $ l $ is a primitive root modulo $ q^t $, and $ \mathrm{ord}_{p^s}(l) = \phi(p^s)/2 $. The form of these cyclotomic classes enabled us to further generalize the results obtained in [1]. The explicit expressions of primitive idempotents of minimal ideals in $ \mathbb{F}_l[x]/\langle x^{p^sq^t}-1\rangle $ were also obtained.
Fields of Study & Subjects
Rings
Modules
and Algebras
Algebraic Geometry and Number Theory
Coding theory and cryptography
Publication details
- Journal / source
- AIMS Mathematics
- Volume
- 11
- Issue
- 4
- Pages
- 10049–10078
- Publication date
- 1 January 2026
- Language
- EN