Additive preservers of rank-additivity on the spaces of symmetric and alternate matrices Original Research Article

Denote the set of n×n symmetric matrices (resp. alternate matrices) over a field F by Sn(F) (resp. Kn(F)). We characterize the bijective additive preservers of rank-additivity on Sn(F) and Kn(F). The set Sn(F) (resp. Kn(F)) forms a non-associative ring with respect to the addition (A,B)maps toA+B and the multiplication (A,B)maps toA·B=ABA where A,Bset membership, variantSn(F) (resp. Kn(F)). The forms of any automorphism of the two non-associative rings are also given.