Maps Preserving Idempotence on Matrix Spaces - Yuqiu Sheng; Hanyu Zhang (Journal of Mathematics)
Suppose F is an arbitrary field. Let |F| be the number of the elements of F. Let Mn(F) be the space of all n×n matrices over F, let Sn(F) be the subset of Mn(F) consisting of all symmetric matrices, and let Tn(F) be the subset of Mn(F) consisting of all upper-triangular matrices. Let V∈{Sn(F),Mn(F),Tn(F)}; a map Φ:V→V is said to preserve idempotence if A-λB is idempotent if and only if Φ(A)-λΦ(B) is idempotent for any A,B∈V and λ∈F. In this paper, the maps preserving idempotence on Sn(F), Mn(F), and Tn(F) were characterized in case |F|=3.