2025/10/15 by S. A. Katre, Katre, S. A, Deepa Krishnamurthi +1
Computer Science · Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Matrix Theory and Algorithms #Number Theory (math.NT) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2510.13469
openalex publication_date 2025/10/15 · openalex created_date 2025/10/17 · openalex updated_date 2026/07/28
It is known that every matrix of order n over the maximal order in an algebraic number eld is a sum of k-th powers in various cases if a discriminant condition is satis ed. It has been proved by Wadikar and Katre that for every matrix of size 2 over maximal orders in rational quaternion division algebras is a sum of squares and cubes. In this paper we consider cyclic division algebras over Q of odd prime degree and show that under some conditions every matrix of size greater equal 2 over these noncommutative rings is a sum of squares and a sum of cubes.