| In recent years, it is one of interesting problems to investigate the invariant of preserving properties of functions, subsets and relations of matrices over various algebraic structures, including fields, rings, and semirings, such as preserving generalized inverse of matices, idempotent matices, matrix ranks and so on..It has been become an active and fertile subject in matrix theory to investigate preserving properties of matrx spaces. From 1991 years,"additive operator"insteading of"linear operator"becomes an important extension, but these all are based on the square matrix, and (besides matrix maps preservers of rank ) the preserving mapping definition can not expand from the square matrix space to the non- square matrix space, in second chapter, in order to extend the maps from the square matrix space to the non- square matrix space, we give the concept of seemingly preserving and break through the limitation of the former definition, we solve the problem of the extension for additive preserver from Mn(F) to Mmn (F), we call the new as seeming preserver maps. In second chapter we give the concept of seemingly preserving {1,2}- inverses additive maps, and the characterization of such maps. the kind of seemingly preserving maps once is introduced, we may abandon its primitive intention, in third and forth chapter, we give the characterization of seemingly preserving Omn(F),where Omn(F) ={ A∣ AT = A+}. |
