On the power polynomial \(x^ d\) over Galois rings
type: Item
instance of: scholarly article
title: On the power polynomial \(x^ d\) over Galois rings
zbMATH Open document ID: 0769.11044
author: Javier Gomez-Calderon
published in: Rocky Mountain Journal of Mathematics
publication date: 1993-05-16T00:00:00Z
review text: For a prime \(p\) let \(GF(p^ n,m)\) denote the Galois ring of order \(p^{mn}\) which can be obtained as a Galois extension of \(\mathbb{Z}_{p^ n}\). The cardinality of the sets \(\{P_ d(x):x\in GR(p^ n,m)\}\) and of the preimage of \(P_ d(x_ 0)\) are determined where \(P_ d(x)=x^ d\). The cases of \(p\) odd and even are treated separately and the enumeration of the preimage cardinality is a function of \(i\) where \(x_ 0=p^ i A\) for \(A\) a unit of \(GF(p^ n,m)\).
Mathematics Subject Classification ID: 11T06
Mathematics Subject Classification ID: 13F25
zbMATH DE Number: 168033
zbMATH Keywords: polynomials
zbMATH Keywords: Galois ring
zbMATH Keywords: cardinality
reviewed by: Ian Blake
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181072701
OpenAlex ID: W2043267763
cites work: Q4046212
DOI: 10.1216/RMJM/1181072701
description: scientific article; zbMATH DE number 168033