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浙江大学学报（理学版）
Journal of Zhejiang University (Science Edition)  2024, Vol. 51 Issue (3): 261-264    DOI: 10.3785/j.issn.1008-9497.2024.03.001
Mathematics and Computer Science     
The images of polynomials with zero constant term on strictly upper triangular matrix algebras
Yingyu LUO1(),Haoliang ZHAO2
1.College of Mathematics，Changchun Normal University，Changchun 130032，China
2.Department of Mathematics，Shanghai Normal University，Shanghai 200234，China
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Abstract  

In the present paper, we define the minimum degree of polynomials. By using the minimum degree of polynomials and Zariski topology, we give a complete description of the images of polynomials with zero constant term on strictly upper triangular matrix algebras over an algebraically closed field.

Key words： polynomial      multilinear polynomial      strictly upper triangular matrix algebra      Zariski topology     
Received: 17 April 2023      Published: 07 May 2024
CLC:  O 151.2  
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Yingyu LUO
Haoliang ZHAO
Cite this article:

Yingyu LUO,Haoliang ZHAO. The images of polynomials with zero constant term on strictly upper triangular matrix algebras. Journal of Zhejiang University (Science Edition), 2024, 51(3): 261-264.

URL:

https://www.zjujournals.com/sci/EN/Y2024/V51/I3/261


常数项为零的多项式在严格上三角矩阵代数上的像

定义了多项式的最小次数。使用多项式的最小次数和Zariski拓扑，给出了代数闭域上常数项为零的多项式在严格上三角矩阵代数上像的完整刻画。


关键词： 多项式,  多重线性多项式,  严格上三角矩阵代数,  Zariski 拓扑 
[1]   FANGUNDES P S. The images of multilinear polynomials on strictly upper triangular matrices［J］. Linear Algebra and Its Applications， 2019， 563： 287-301. DOI：10.1016/j.laa.2018.11.014
doi: 10.1016/j.laa.2018.11.014
[2]   WANG Y， ZHOU J， LUO Y Y. The image of polynomials on 2 × 2 upper triangular matrix algebras［J］. Linear Algebra and Its Applications， 2021， 610： 560-573. DOI：10.1016/j.laa.2020.10.009
doi: 10.1016/j.laa.2020.10.009
[3]   CHEN Q， LUO Y Y， WANG Y. The image of polynomials on 3 × 3 upper triangular matrix algebras［J］. Linear Algebra and Its Applications， 2022， 648： 254-269. DOI：10.1016/j.laa.2022.05.010
doi: 10.1016/j.laa.2022.05.010
[4]   PANJA S， PRASAD S. The image of polynomials and Waring type problems on upper triangular matrix algebras［J］. Journal of Algebra， 2023， 631： 148-193. DOI：10.1016/j.jalgebra.2023.04.027
doi: 10.1016/j.jalgebra.2023.04.027
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