WITHDRAWN: Images of arbitrary polynomials on upper triangular matrix algebras

Chen, Qian; Wang, Yu

doi:10.1016/j.jalgebra.2022.10.038

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2022

2023

Publication Types

Select...

Article2

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

(1 citation statement)

References 47 publications

(41 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We organize the paper as follows: In Section 2 we shall give some prelimiaries. We shall slightly modify some results in [5,7,12], which will be used in the proof of Theorem 1.2. In Section 3 we shall give the proof of Theorem 1.2 by using some new arguments, for example, the compatibility of variables and recursive polynomials.…”

Section: Introductionmentioning

confidence: 99%

Prediction of Pediatric Sepsis Using a Deep Encoding Network with Cross Features

Chen

Zhang

Tang

et al. 2022

J. Shanghai Jiaotong Univ. (Sci.)

View full text Add to dashboard Cite

In the present paper we shall investigate the Waring's problem for upper triangular matrix algebras. The main result is the following: Let n ≥ 2 and m ≥ 1 be integers. Let p(x 1 , . . . , xm) be a noncommutative polynomial with zero constant term over an infinite field K. Let Tn(K) be the set of all n × n upper triangular matrices over K. Suppose 1 < r < n − 1, where r is the order of p. We have that p(Tn(K)) + p(Tn(K)) = J r , where J is the Jacobson radical of Tn(K). If r = n − 2, then p(Tn(K)) = J n−2 . This gives a definitive solution of a conjecture proposed by Panja and Prasad.

show abstract

Section: Introductionmentioning

confidence: 99%