Matrices over non-commutative rings as sums of powers

被引：1

作者：

Katre, S. A. ^{[1
]}

Krishnamurthi, Deepa ^{[2
]}

机构：

[1] Savitribai Phule Pune Univ, Pune, Maharashtra, India

[2] St Miras Coll Girls, Pune, Maharashtra, India

来源：

LINEAR & MULTILINEAR ALGEBRA | 2022年 / 70卷 / 05期

关键词：

Matrices; non-commutative rings; trace; sums of powers; Waring's problem;

D O I：

10.1080/03081087.2020.1748856

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let R be non-commutative ring with unity and n >= p >= 2, p prime. In this paper, we prove that an n x n matrix over R is the sum of pth powers if and only if its trace can be written as a sum of pth powers and commutators modulo pR. This extends the results of L. N. Vaserstein (p = 2) and S. A. Katre, Kshipra Wadikar (p = 3). We also obtain necessary and sufficient conditions for a matrix over R to be written as a sum of fourth powers when n >= 2.

引用

页码：824 / 829

页数：6

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