Year: 2006
Type: article
Abstract: In [2], they found some natural generators for the ideals of the finite ring $Z_{pm}$ [X]/ $(X^n\;-\;1)$ , where p and n are relatively prime. If p and n are not relatively prime $X^n\;-\;1$ is not a product of basic irreducible polynomials but a product of primary polynomials. Due to this fact, to consider the ideals of $Z_{pm}$ [X]/ $(X^n\;-\;1)$ in 'inseparable' case we need to look at the primary ideals of $Z_{pm}$ [X]. In this paper, we find a set of generators of ideals of $Z_{pm}$ [X]/(f) for some primary polynomials f of $Z_{pm}$ [X].
Author: Sung-Sik Woo
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W884031534