Year: 2026
Type: preprint
Abstract: Let $R$ be non-commutative ring with unity. In this paper, we prove that a given matrix in $M_n(R)$ is a sum of $p$-th powers in $M_n(R)$, where $n < p$ if and only if its trace can be written as a sum of $p$-th powers in $M_n(R)$, for $n = 2,3,4$ and $p = 5$ and $n = 4,5,6$ for $p = 7$. This paper extends the results of S. A. Katre and Kshipra Wadikar, $(p=3)$ and Garge $(n \geq p), (p = 5, 7)$, and S. A. Katre and Deepa Krishnamurthi $(n \geq p)$.
Source: arXiv (Cornell University)
Authors: Kochrekar, Tanay, Garge, A. S.
Institution: University of Mumbai
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213274543