On a characterization of complete matrix rings |
| |
Authors: | Leon van Wyk |
| |
Institution: | (1) Department of Mathematics, University of Stellenbosch, Matieland, Private Bag-X1, 7602, South Africa |
| |
Abstract: | Peter R. Fuchs established in 1991 a new characterization of complete matrix rings by showing that a ringR with identity is isomorphic to a matrix ringM
n
(S) for some ringS (and somen 2) if and only if there are elementsx andy inR such thatx
n–1 0,x
n=0=y
2,x+y is invertible, and Ann(x
n–1)Ry={0} (theintersection condition), and he showed that the intersection condition is superfluous in casen=2. We show that the intersection condition cannot be omitted from Fuchs' characterization ifn3; in fact, we show that if the intersection condition is omitted, then not only may it happen that we do not obtain a completen ×n matrix ring for then under consideration, but it may even happen that we do not obtain a completem ×m matrix ring for anym2. |
| |
Keywords: | Primary 16S50 |
本文献已被 SpringerLink 等数据库收录! |
|