Linear Operators Preserving Idempotent Matrices Over Division Rings

Many authors have studied the problem of determining the linear operators, on the n×n matrix algebra Mn（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 R1 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 Mn（R） into Mn（R1） where Mn（R）