Linear/additive preservers of rank 2 on spaces of alternate matrices over fields

Let K, (F) be the linear space of all n x n alternate matrices over a field F, and let K-n(2)(F) be its subset consisting of all rank-2 matrices. An operator phi : K-n(F) --> K-n(F) is said to be additive if phi (A + B) = phi (A) + phi (B) for any A, B is an element of K-n (F), linear if phi is additive and phi (a A) = af (A) for every a is an element of F and A is an element of K-n (F), and a preserver of rank 2 on K-n (F) if phi (K-n(2)(F)) subset of or equal to K-n(2)(F). When n greater than or equal to 4, we characterize all linear (respectively, additive) preservers of rank 2 on K-n (F) over any field (respectively, any field that is not isomorphic to a proper subfield of itself). (C) 2004 Elsevier Inc. All rights reserved.