Let D be an arbitrary division ring and Mn(D) be the set of all n × n matrices over D. We define the rank subtractivity or minus partial order on Mn(D) as defined on Mn(C), i.e., A B iff rank(B) = rank(A)+rank(B−A). We describe the structure of maps Φ on Mn(D) such that A B iff Φ(A) Φ(B)(A,B ∈ Mn(D)).
