"Matrix  mappings  preserving  Diedonne  determinant  and  their
 algorithmic constructions"

Elena Kreines
Department of Mechanics and Mathematics, Moscow State University.



     ABSTRACT.

     In this paper the following problem is considered: let  $D$
be a skew-field, $M_n(D)$ be a matrix algebra  over  its  center
$K$. A classification of  one-to-one  $K$-linear  mappings  from
$M_n(D)$ to $M_n(D)$ which  preserves  Diedonne  determinant  is
obtained. Namely,  $T(A)=P(A^s)Q$  for  all  matrices  $A$  from
$M_n(D)$ or $T(A)=P( (A^s)^t  )Q$  for  all  matrices  $A$  from
$M_n(D)$, here  $s$  denotes  $K$-linear  authomorphism  of  the
skew-field $D$, and $t$ denotes transpose matrix.
     Computational algorithms for constracting matrices  $P$  and
$Q$ are proposed.