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Research Article | Open Access

The image of polynomials in one variable on 2 × 2 upper triangular matrix algebras

Lan Lu1, Yu Wang2( ), Huihui Wang2, Haoliang Zhao2
Department of Basic Courses, Changchun Guanghua University, Changchun 130033, China
Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
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Abstract

In the present paper, we give a description of the image of polynomials in one variable on 2 × 2 upper triangular matrix algebras over an algebraically closed field. As consequences, we give concrete descriptions of the images of polynomials of degrees up to 4 in one variable on 2 × 2 upper triangular matrix algebras over an algebraically closed field.

Keywords

polynomialupper triangular matrix algebraalgebraically closed field
CLC number: 16S50, 16R10, 15A54

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AIMS Mathematics
Volume 7 Issue 6,
June 2022
Pages 9884-9893
DOI: 10.3934/math.2022551

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Cite this article:
Lu L, Wang Y, Wang H, et al. The image of polynomials in one variable on 2 × 2 upper triangular matrix algebras. AIMS Mathematics, 2022, 7(6): 9884-9893. https://doi.org/10.3934/math.2022551

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Received: 26 December 2021
Revised: 19 February 2022
Accepted: 27 February 2022
Published: 15 June 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)