Critical polynomials related to generalized derivations
type: Item
instance of: scholarly article
title: Critical polynomials related to generalized derivations
zbMATH Open document ID: 1031.15031
DOI: 10.1016/S0024-3795(03)00417-8
author: J. A. Dias Da Silva
author: Hemar Godinho
published in: Linear Algebra and its Applications
publication date: 2003-08-25T00:00:00Z
review text: The authors [ibid. 342, 1--15 (2002; Zbl 1026.11030)] have shown that, if \(V\) is a vector space and \(T\) is a linear operator on \(V\) with minimal polynomial of degree \(n\), then, \[ \left[\frac{m(n-1)}{k} \right]+1 \] is a lower bound for the degree of the minimal polynomial of the \(k\)-derivation of \(T\) on \(\otimes^m V\). Also some correlations between generalized derivations and problems in additive number theory may be found there. In the present paper the authors study the structure of the linear operators \(T\), whose minimal polynomial of the \(k\)-derivation has degree precisely equal to the bound above.
reviewed by: Ivan V. Arzhantsev
Mathematics Subject Classification ID: 15A72
Mathematics Subject Classification ID: 11B75
Mathematics Subject Classification ID: 15A69
Mathematics Subject Classification ID: 15A18
zbMATH DE Number: 1970628
zbMATH Keywords: minimal polynomial
zbMATH Keywords: tensor powers of a linear operator
zbMATH Keywords: critical operators
zbMATH Keywords: generalized derivations
MaRDI profile type: Publication
cites work: Q4664539
cites work: Generalized derivations and additive theory
cites work: Q4771383
description: scientific article; zbMATH DE number 1970628