Some remarks on the primary ideals of $\Bbb Z_{p^m}[X]$

Abstract

In [2], they found some natural generators for theideals of the nite ring Zpm [X ]=(X n 1), where p and n arerelatively prime. Ifp and n are not relatively prime X n 1 isnot a product of basic irreducible polynomials but a product ofprimary polynomials. Due to this fact, to consider the ideals ofZpm [X ]=(X n 1) in `inseparable' case we need to look at the pri-mary ideals of Zpm [X ]. In this paper, we nd a set of generators ofideals of Zpm [X ]=(f) for some primary polynomials f of Zpm [X ].