Table of Contents
Algebra
Volume 2014 (2014), Article ID 745029, 6 pages
http://dx.doi.org/10.1155/2014/745029
Research Article

The Matrix Equation over Fields or Rings

GAATI, Université de la polynésie française, BP 6570, 98702 Faa’a, Tahiti, French Polynesia

Received 1 June 2014; Revised 9 September 2014; Accepted 16 September 2014; Published 1 October 2014

Academic Editor: Zhongshan Li

Copyright © 2014 Gerald Bourgeois. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let and let be an algebraically closed field with characteristic 0 or greater than . We show that if and satisfy , then are simultaneously triangularizable. Let be a reduced ring such that is not a zero divisor and let be a generic matrix over ; we show that is the sole solution of . Let be a commutative ring with unity; let be similar to such that, for every is not a zero divisor. If is a nilpotent solution of where , then .