摘要
Many authors have studied the problem of determining the linear operators, on the n×n matrix algebra M<sub>n</sub>(R) over a commutative R, which preserve idempotent matrices (see Refs. [1]—[4]). In this note, we make a start on the noncommutative case. If R and R<sub>1</sub> are division rings and their characteristic numbers are not 2 and their centers are the same field F. Let T denote an F-linear operator which maps M<sub>n</sub>(R) into M<sub>n</sub>(R<sub>1</sub>) where M<sub>n</sub>(R)