Linear recurring sequences over modules
type: Item
instance of: scholarly article
title: Linear recurring sequences over modules
zbMATH Open document ID: 0854.11067
DOI: 10.1007/BF00047168
published in: Acta Applicandae Mathematicae
publication date: 1997-01-19T00:00:00Z
review text: The paper is devoted to the following generalization of the concept of the linear recurring sequence. Let \(M\) be an \(R\)-module over a commutative ring with identity. Let \(M^{\langle k\rangle}\) be the set of all \(k\)-sequences, i.e. functions \(\mu: \mathbb{N}_0^k\to M\). A sequence \(\mu\in M^{\langle k\rangle}\) is called a \(k\)-linear recurring sequence over \(M\) if the annihilator of \(\mu\) in the ring of polynomials of \(k\) variables contains \(k\) monic polynomials \(F_1 (x_1), \dots, F_k (x_k)\) of one variable and with specified multiplication of polynomials and \(k\)-sequences. In the paper some fundamental results of the theory of \(k\)-linear recurring sequences over rings and modules (e.g. quasi-Frobenius modules or Galois rings) are collected, thereby giving an overview of the work done in the direction of the extension of the theory of linear recurrences over fields to this more general setting. (The paper contains a list of references consisting of 112 items).
Mathematics Subject Classification ID: 11T06
Mathematics Subject Classification ID: 11B37
Mathematics Subject Classification ID: 11T71
Mathematics Subject Classification ID: 16L60
Mathematics Subject Classification ID: 94A60
Mathematics Subject Classification ID: 94B05
zbMATH DE Number: 841769
zbMATH Keywords: periodic sequence
zbMATH Keywords: linear recurring sequence
zbMATH Keywords: quasi-Frobenius modules
zbMATH Keywords: Galois rings
author: A. V. Mikhalev
author: Alexander Nechaev
reviewed by: Štefan Porubský
MaRDI profile type: Publication
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Linear recurring sequences over modules (full work available at URL)
full work available at URL: https://doi.org/10.1007/bf00047168

Linear recurring sequences over modules (OpenAlex ID)
OpenAlex ID: W1972925812