SOME REMARKS ON THE PRIMARY IDEALS OF ℤpm[X]

Title & Authors
SOME REMARKS ON THE PRIMARY IDEALS OF ℤpm[X]
Woo, Sung-Sik;

Abstract
In [2], they found some natural generators for the ideals of the finite ring $\small{Z_{pm}}$[X]/$\small{(X^n\;-\;1)}$, where p and n are relatively prime. If p and n are not relatively prime $\small{X^n\;-\;1}$ is not a product of basic irreducible polynomials but a product of primary polynomials. Due to this fact, to consider the ideals of $\small{Z_{pm}}$[X]/$\small{(X^n\;-\;1)}$ in `inseparable` case we need to look at the primary ideals of $\small{Z_{pm}}$[X]. In this paper, we find a set of generators of ideals of $\small{Z_{pm}}$[X]/(f) for some primary polynomials f of $\small{Z_{pm}}$[X].
Keywords
primary ideal;polynomial over a finite ring;
Language
English
Cited by
References
1.