Waring's problem for matrices over orders in algebraic number fields
| dc.creator | Gadre, A. S. | |
| dc.creator | Katre, S. A. | |
| dc.date | 2007-02-15 | |
| dc.date.accessioned | 2026-07-07T07:47:04Z | |
| dc.date.available | 2026-07-07T07:47:04Z | |
| dc.description | In this paper we give necessary and sufficient trace conditions for an n by n matrix over any commutative and associative ring with unity to be a sum of k-th powers of matrices over that ring, where n,k are integers greater equal 2. We prove a discriminant criterion for every 2 by 2 matrix over an order R to be sums of cubes and fourth powers over R. We also show that if q is a prime and n greater equal 2, then every n by n matrix over the ring of integers O, of a quadratic number field is a sum of q-th powers (of matrices) over O if and only if q is coprime to the discriminant of the quadratic number field. | |
| dc.description | 9 pages, No figures | |
| dc.identifier | https://arxiv.org/abs/math/0702445 | |
| dc.identifier | http://arxiv.org/abs/math/0702445 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/124043 | |
| dc.subject | Number Theory | |
| dc.subject | 11R04, 11R11, 11R29, 15A33 | |
| dc.title | Waring's problem for matrices over orders in algebraic number fields | |
| dc.type | text |