Additive rank-one nonincreasing maps on Hermitian matrices over the field GF(4)

Abstract

Abstract.A complete classification of additive rank-one nonincreasing maps on hermitian matrices over Galois field GF (2 2 ) is obtained. This field is special and was not covered in a previous paper. As a consequence, some known applications, like the classification of additive rank-additivity preserving maps, are extended to arbitrary fields. An application concerning the preservers of hermitian varieties is also presented.