CAJ | 학술논문

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)],(V)[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.
설F표시역,n시대우등우4적정수.Kn(F)시유역상적소유n계교착구진구성적집합.설fij(i,j=1.2,…,n)시F도F상적영사,f시Kn(F)도Kn(F)적영사병차영사적형식피정의위f:[aij]|→[fij(aij)],(V)[aij]∈Kn(F)칙f칭위fij(i,j=1,2,…,n)유도적영사(즉도출영사).급출료역상교착구진공간보질2도출영사적각화.
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: [aij] →[fij (aij)] for any[aij] ∈ Kn (F), then we say that f is produced by fij.The general form of all mapsf:Kn(F)→Kn(F) produced by fij preserving rank-2 alternate matrices and satisfies f(0) = O is characterized.