域上交错矩阵空间的保秩导出映射(英文)

Maps preserving rank-2 alternate matrices over fields

设F表示域,n是大于等于4的整数。Kn(F)是由域上的所有n阶交错矩阵构成的集合。设fij(i,j=1,2,…,n)是F到F上的映射,f是Kn(F)到Kn(F)的映射,并且映射的形式被定义为f:[aij]|→[fij(aij)],[aij]∈Kn(F)则f称为fij(i,j=1,2,…,n)诱导的映射(即导出映射)。给出了域上交错矩阵空间保秩2导出映射的刻画。

Suppose F is an arbitrary field,n be an integer with n≥4.Denote by Kn（F） the set of all n×n alternate matrices over F.Let fij（i,j=1,2,…,n） be maps from F to itself.If a map f：Kn（F）→Kn（F） is defined by f：｜→[fij（aij）] for any∈Kn（F）,then we say that f is produced by fij.The general form of all maps f：Kn（F）→Kn（F） produced by fij preserving rank-2 alternate matrices and satisfies f（0）=0 is characterized.