Direct factors of polynomial rings over finite fields
type: Item
instance of: scholarly article
title: Direct factors of polynomial rings over finite fields
zbMATH Open document ID: 0591.12020
DOI: 10.1016/0097-3165(85)90102-5
author: John Knopfmacher
published in: Journal of Combinatorial Theory. Series A
publication date: 1985-01-01T00:00:00Z
review text: An asymptotic formula is derived for the total number of polynomials of degree n in an arbitrary direct factor of the set G of all monic polynomials in one unknown over a finite field with q elements. A direct factor of G is a subset \(B_ 1\) of G such that for some subset \(B_ 2\) of G, every polynomial w in G has a unique factorization of the form \(w=b_ 1b_ 2\), where \(b_ i\in B_ i\). The asymptotic formula is given as \(c_ 1q^ n\), where \(c_ 1\) is a constant depending on \(B_ 1\).
reviewed by: Joseph J. Liang
Mathematics Subject Classification ID: 11T06
Mathematics Subject Classification ID: 11N45
zbMATH DE Number: 3948426
zbMATH Keywords: asymptotic formula
zbMATH Keywords: finite field
zbMATH Keywords: polynomial
MaRDI profile type: Publication
full work available at URL: 0097-3165(85)90102-5
OpenAlex ID: W2014226081
cites work: On the Density of Direct Factors of the Set of Positive Integers
cites work: Q3839703
description: scientific article; zbMATH DE number 3948426