Open AccessThe image of polynomials in one variable on $ 2\times 2 $ upper triangular matrix algebras
Author(s) -
Lixin Lu,
Yu Wang,
Huihui Wang,
Hongguang Zhao
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022551
Subject(s) - algebraically closed field , triangular matrix , mathematics , variable (mathematics) , image (mathematics) , matrix (chemical analysis) , field (mathematics) , pure mathematics , combinatorics , algebra over a field , mathematical analysis , computer science , computer vision , chemistry , invertible matrix , chromatography
In the present paper, we give a description of the image of polynomials in one variable on $ 2\times 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\times 2 $ upper triangular matrix algebras over an algebraically closed field.